1.
Structural Design and Optimization
Part II – V edition, 2023
Prof. Ing. Franco Bontempi
Docente di TEORIA E PROGETTO DI PONTI – GESTIONE DI PONTI E GRANDI STRUTTURE
Facoltà di Ingegneria Civile e Industriale
Università degli Studi di Roma La Sapienza
franco.bontempi@uniroma1.it
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 2
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 3
Abstract
• Structural engineering can nowadays make use of very remarkable computational
tools. This availability can lead to affirm that the entire process of designing and
verifying the quality of a structure can be automated.
• Paradoxically, the opposite is true: powerful tools require deep reflections on what
are the bases of structural design in order to consciously address the procedures
of representation and optimization available today.
• In this only in this way, that optimization can represent an effective fundamental
component of structural design, in order to try to maximize the performance of
the structures and their sustainability.
• In order to obtain a correct optimization, it is therefore necessary to examine the
roots of the design, to understand its meanings and evaluate the limits of the
different numerical implementations.
• The lessons of the course will develop the concepts underlying structural
optimization while presenting specific significant applications
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 4
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 5
• Monday 30 January
15.00-18.00 (3 hours)
• Prof. Franco Bontempi
• Basis of structural design
• The art of structural engineering. The
principles of design. The creative process.
Structural concept. Design context and
structural requirements. Structural values.
Design by evolution and innovation.
Integration and specialization. Path of
loads. Structural schemes and their limits.
Structural analysis.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 6
DAY 1
• D. Billington, The Tower and the Bridge: The New Art of
Structural Engineering
• E. S. Ferguson, Engineering and the Mind’s Eye.
• H. Simon, The Science of Artificial.
• G. Madhavan, Come pensano gli ingegneri. Intelligenze
applicate.
• B. Munari, Da cosa nasce cosa. Appunti per una
metodologia progettuale.
• P. L. Nervi, Scienza o arte del costruire?
• E. Torroja, La concezione Strutturale.
• L.E. Robertson, The Structure of Design.
• W. Lidwell, K. Holden, J. Butler, Universal Principle of Design.
• U. Kirsch, Structural Optimization. Fundamentals and
Applications.
• S. Adriaenssens, P. Block, D. Veenendaal, C.Williams. Shell
Structures for Architecture: Form Finding and Optimization.
• M. Sarkisian, Designing Tall Buildings: Structure as
Architecture.
• Tuesday 31 January
10.00-13.00 (3 hours)
• Prof. Franco Bontempi
• Qualitative and quantitative aspects of
structural optimization
• Setting up the structural problem.
Uncertainties and undefinitions. Limited
rationality and partial knowledge.
Structural modeling. Solution of the
structural problem and its critical
judgment. Naïve setting of optimization
problems. Optimization algorithms.
Stochastic aspects. Heuristic approaches.
Discrete structural schemes.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 7
DAY 2
• Tuesday 31 January
15.00-18.00 (3 hours)
• Dr. Valentina Tomei
• Optimization strategies for the design of
gridshell type structures
• Notes on the types of structural optimization
and on the single-objective and multi-
objective optimization algorithms of an
evolutionary type. Notes on strategies for
finding the optimal shape: form-finding.
Gridshell type structures. The role of form in
gridshells. The role of structural optimization
in gridshell design: examples of design
strategies.
• Wednesday 1st February
15.00-18.00 (3 hours)
• Prof. Elena Mele
• Optimization of structures for tall
buildings
• Behavior of tall buildings, "premium for
height" and structural types. Notes on the
evolution of the structural design of tall
buildings and recent trends: the search for
efficiency and the role of robustness.
Diagrid structures and structural patterns:
sectional and topological optimization.
Patterns inspired by isostatic lines.
Generative design and shape grammar.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 8
DAY 3
• Wednesday 1st February
10.00-13.00 (3 hours)
• Prof. Francesco Petrini
• Optimization in the performance design of
buildings under wind action and seismic
action
• Application of optimization methods to real
problems. Performance-based design: general
aspects and specific characteristics.
Optimization of devices for the control of
vibrations of tall buildings under the action of
the wind. Risk-based design of reinforced
concrete frames in seismic zone with
development of an optimization procedure
based on the gradient method.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 9
DAY 4
• Thursday 2nd February
10.00-13.00 (3 hours)
• Dr. Innocenzo Becci
• Seismic recovery of prefabricated buildings
with the use of dissipation systems and
decoupling systems
• With a technical practice setting, the
presentation concerns the seismic
improvement design approach on
prefabricated structures with the use of
mechanical connection and dissipation
devices. For the typological conception of the
mechanisms and for the materials used in the
systems, the selection criteria and the
experiences of experimental feedback which
have made it possible to validate the expected
operating principles will be exposed.
• Thursday 2nd February
15.00-18.00 (3 hours)
• Prof. Arch. Patrizia Trovalusci
• The construction of form in architectural
works: critical issues and advantages of
the mathematical/numerical approach
• The lesson presents, explores and
discusses mainly qualitative aspects
concerning works of architecture and is
accompanied by some examples of study
addressed in some degree theses (which
are available at this link:
https://sites.google.com/a/uniroma1.it/pa
triziatrovalusci/tesi-di-laurea/tesi-di-
laurea-sdc)
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 10

2.
• Tuesday 26 October 10.00-13.00 (3 hours)
• Prof. Franco Bontempi
• Qualitative and quantitative aspects of
structural optimization
• Setting up the structural problem.
Uncertainties and undefinitions. Limited
rationality and partial knowledge.
Structural modeling. Solution of the
structural problem and its critical
judgment. Naïve setting of optimization
problems. Optimization algorithms.
Stochastic aspects. Heuristic approaches.
Discrete structural schemes.
• Tuesday 26 October 15.30-18.30 (2 hours)
• Prof. Arch. Patrizia Trovalusci
• The construction of form in architectural
works: critical issues and advantages of
the mathematical/numerical approach
• The lesson presents, explores and
discusses mainly qualitative aspects
concerning works of architecture and is
accompanied by some examples of study
addressed in some degree theses (which
are available at this link:
https://sites.google.com/a/uniroma1.it/pa
triziatrovalusci/tesi-di-laurea/tesi-di-
laurea-sdc)
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 11
DAY 2
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 12
FORMULABILE
NON
FORMULABILE
Esprimibile in equazioni
HARD
RESTRICTED
Non esprimibile in equazioni
SOFT
WIDE
Prima
lezione
Seconda
lezione
NON
FORMULABILE
Non esprimibile in equazioni
SOFT
WIDE
Prima
lezione
8. Constructive approach
• Insight in a structural problem
• Simple observations
9. Algorithms
• Direct way: basic aspects
• Surrogate
• Not so basic aspects
• Heuristics
• In another (indirect) way:
optimality criteria
10.Levels in action
• Sizing
• Morphology
• Topology
• Generative
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 13
Index Part II
1983
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 14
CONSTRUCTIVE APPROACH
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 15
8
CONSTRUCTIVE APPROACH
STRUCTURAL DESIGN AND OPTIMIZATION 2023 16
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
17
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 18
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
19
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
INSIGHT
IN A STRUCTURALPROBLEM
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 20

3.
Load Path
21
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
1
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 22
Load Transfer Mechanism
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 23
2
29-Jan-23 24
STRUCTURAL DESIGN AND OPTIMIZATION 2023
1 - Strutture resistenti per forma
29-Jan-23
In tutta la struttura c'è solo o trazione o compressione
STRUCTURAL DESIGN AND OPTIMIZATION 2023 25 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 26
2 - Strutture resistenti per azione vettoriale
29-Jan-23
Nella struttura ci sono elementi che lavorano uniformemente
a trazione o a compressione (tiranti o puntoni)
STRUCTURAL DESIGN AND OPTIMIZATION 2023 27 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 28
3 - Strutture resistenti per flessione
29-Jan-23
Nelle sezioni della struttura c'è sia trazione sia compressione
(diagramma degli sforzi a farfalla)
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 30

4.
4 - Strutture resistenti per superficie
29-Jan-23
La struttura distribuisce ed equilibra i carichi con azione membranale
(distribuzione di sforzo uniforme sullo spessore)
STRUCTURAL DESIGN AND OPTIMIZATION 2023 31 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 32
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 33
Structural System
34
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
3
35
x
x
x
x
Fault
Fault
Fault
Fault
Overall plant
1st level
Plant item
2nd level
Control loop
3rd level
Element/Component
4th level
STRUTTURA
GLOBALE
SOTTO-STRUTTURA
2 livello
ELEMENTO STRUTURALE
3 livello
COMPONENTE
4 livello
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 36
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 37 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 38
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 39
Es.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 40

5.
MAIN
STRUCTURAL
SYSTEM
AUXILIARY
STRUCTURAL
SYSTEM
SECONDARY
STRUCTURAL
SYSTEM
SPECIAL
DECK ZONES
BRIDGE
DECK
HIGHWAY SYSTEM
RAILWAY SYSTEM
OPERATION
MAINTENANCE
EMERGENCY
FOUNDATION OF TOWERS
TOWERS
ANCHORAGES
SUPPORTING
CONDITION
HIGHWAY BOX-GIRDER
CROSS BOX-GIRDER
RAILWAY BOX-GIRDER
INNER
OUTER
BRIDGE
SUPERSTRUCTURE
MACRO-LEVELS
MESO-LEVELS
MAIN CABLES
HANGERS
SUSPENSION
SYSTEM
SADDLES
OUTER
HIGHWAY BOX-GIRDER
CROSS BOX-GIRDER
RA
R
R ILWAY BOX-GIRDER
FOUN
U
U DATION OF TOWERS
TOWERS
AN
A
A CHORA
R
R GES
MAIN CABLES
SADDLES
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 41
Structures Essentials
• Micro-level:
local size of the sections, i.e., thickness, area, inertia, … (Detailed
Geometry)
• Meso-level:
form of the structural element or structural part (substructure), i.e.
main longitudinal axis, curvature, profile, … (Global Geometry)
• Macro-level:
connections of the different structural parts (Load Path)
42
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
local size of the sections, i.e., thickness, area, inertia, … (Detailed
4
http://carat.st.bv.tum.de/caratuserswiki/index.php/Users:Structural_Optimization/General_Formulation
Optimization Levels (1)
43
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
http://carat.st.bv.tum.de/caratuserswiki/index.php/Users:Structural_Optimization/General_Formulation
Optimization Levels (2)
Micro-level:
local size of the sections,
i.e. thickness, area,
inertia, … (Detailed
Geometry)
Meso-level:
form of the structural
element or structural part
(substructure), i.e. main
longitudinal axis, curvature,
profile, … (Global Geometry)
Macro-level:
connections of the
different structural
parts (Load Path)
44
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
SIMPLE OBSERVATIONS
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 45 46
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
47
47
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
The nature of optimum (1)
48
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Example (1)
49
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Example (2)
50
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023

6.
51
Robustness of the formulation
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 52
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
The nature of optimum (2)
A sub-optimal solution
to a problem is one
that is less than perfect.
Slack situation: loose and not pulled tight.
53
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 54
Limiti approssimativi abbastanza larghi
ALGORITHMS
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 55
9
STRUCTURAL DESIGN AND OPTIMIZATION 2023
DIRECT WAY: BASIC ASPECTS
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 56
57
Direct
Approach
for
Optimization
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 58
1D
function
–
Line
Optimization
(1
direction)
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Bracketing of the minimum
59
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
1° step
Δ1
βΔ1
a1 b1
c1
f(x)
x
60
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023

7.
2° step
Δ2
βΔ2
a2
b2
c2
f(x)
x
61
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
3° step
Δ3
βΔ3
a3
b3
c3
f(x)
x
β=0.61803
62
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Quadratic Fitting
63
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 64
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
65
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Bracketing with parabolic interpolation
66
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Cubic Fitting
67
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 68
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
69
Convergence
Criteria
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 70
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023

8.
71
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 72
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
73
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 74
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
75
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 76
Searching in the good direction
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
77
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Scaling of Design Variables
• It is often desirable to eliminate wide variations in the magnitudes
of design variables and the value of constraints by normalization.
• Design variables may be normalized to order 1 by scaling.
• This operation may enhance the efficiency and reliability of the
numerical optimization process.
78
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
79
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 80
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023

9.
81
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
SURROGATE
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 82
83
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Design of Experiments (DOE)
84
• In general usage, design of experiments (DOE) or experimental design is the
design of any information-gathering exercises where variation is present,
whether under the full control of the experimenter or not. However, in
statistics, these terms are usually used for controlled experiments.
• Formal planned experimentation is often used in evaluating physical objects,
chemical formulations, structures, components, and materials.
• Other types of study, and their design, are discussed in the articles on
computer experiments, opinion polls and statistical surveys (which are types
of observational study), natural experiments and quasi-experiments (for
example, quasi-experimental design).
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Sampling Points (1)
85
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Sampling Points (2)
86
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Simulation & Approximation of the Response
87
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
The Function: y(x1,x2)
88
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
The Sensibility of the Function
89
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
STRATEGY #1: SENSITIVITY - Governance of Priorities
90
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023

10.
The Bounding of the Function
91
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
STRATEGY #2: BOUNDING - Behavior Governance
p
l(p)
l
p
l(p)
l
92
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
NOT SO BASIC ASPECTS
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 93 94
Relative
Gain
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
1
95
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 96
96
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
97
97
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 98
98
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 99
A decision point in the development of the solution
100
100
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023

11.
101
101
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Multilevel Optimal Design
102
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
2
Decomposition
103
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Multilevel Structures
104
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
105
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 106
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
107
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 108
1997
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 109
HEURISTICS
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 110

12.
Heuristics
• A heuristic technique (/hjᵿˈrɪstᵻk/; Ancient Greek: εὑρίσκω, "find"
or "discover"), often called simply a heuristic, is any approach to
problem solving, learning, or discovery that employs a practical
method not guaranteed to be optimal or perfect, but sufficient for
the immediate goals.
• Where finding an optimal solution is impossible or impractical,
heuristic methods can be used to speed up the process of finding a
satisfactory solution.
• Heuristics can be mental shortcuts that ease the cognitive load of
making a decision.
111
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
εὑρίσκω
• Heuristic (/hjʉˈrɪstɨk/; Greek: "Εὑρίσκω", "find" or "discover")
refers to experience-based techniques for problem solving,
learning, and discovery that give a solution which is not
guaranteed to be optimal. Where the exhaustive search is
impractical, heuristic methods are used to speed up the process of
finding a satisfactory solution via mental shortcuts to ease the
cognitive load of making a decision. Examples of this method
include using a rule of thumb, an educated guess, an intuitive
judgment, stereotyping, or common sense.
• In more precise terms, heuristics are strategies using readily
accessible, though loosely applicable, information to control
problem solving in human beings and machines.
112
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
εὑρίσκω
• L'euristica (dalla lingua greca εὑρίσκω, letteralmente "scopro" o
"trovo") è una parte dell'epistemologia e del metodo scientifico.
• Si definisce procedimento euristico, un metodo di approccio alla
soluzione dei problemi che non segue un chiaro percorso, ma che
si affida all'intuito e allo stato temporaneo delle circostanze, al fine
di generare nuova conoscenza. È opposto al procedimento
algoritmico. In particolare, l'euristica di una teoria dovrebbe
indicare le strade e le possibilità da approfondire nel tentativo di
rendere una teoria progressiva.
113
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Bounded Rationality
• Bounded rationality is the idea that in decision-making, rationality of
individuals is limited by the information they have, the cognitive limitations
of their minds, and the finite amount of time they have to make a decision.
• It was proposed by H. A. Simon as an alternative basis for the mathematical
modeling of decision making, as used in economics, …; it complements
rationality as optimization, which views decision-making as a fully rational
process of finding an optimal choice given the information available.
• Another way to look at bounded rationality is that, because decision-makers
lack the ability and resources to arrive at the optimal solution, they instead
apply their rationality only after having greatly simplified the choices
available. Thus, the decision-maker is a satisfier, one seeking a satisfactory
solution rather than the optimal one.
114
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 115 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 116
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 117 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 118
1
119
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Simulated Annealing (Metropolis)
• Simulated annealing (SA) is a generic probabilistic heuristic for the global
optimization problem of locating a good approximation to the global optimum of a
given function in a large search space.
• The name and inspiration come from annealing in metallurgy, a technique
involving heating and controlled cooling of a material to increase the size of its
crystals and reduce their defects.
• This notion of slow cooling is implemented in the Simulated Annealing algorithm
as a slow decrease in the probability of accepting worse solutions as it explores the
solution space. Accepting worse solutions is a fundamental property of heuristics
because it allows for a more extensive search for the optimum.
• The method is an adaptation of the Metropolis-Hastings algorithm, a Monte Carlo
method to generate sample states of a thermodynamic system, invented by M.N.
Rosenbluth and published in a paper by N. Metropolis et al. in 1953.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 120

13.
121
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Basic version (1)
122
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Basic version (2)
123
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 124
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
125
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Points for SA
• Diameter of the search graph
• Transition probabilities
• Acceptance probabilities
• Efficient candidate generation
• Barrier avoidance
• Cooling schedule
126
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
127
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 128
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
129
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
2
130
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023

14.
Nelder-Mead Method (Amoeba)
• The Nelder–Mead method or downhill simplex method or amoeba
method is a commonly used nonlinear optimization technique,
which is a well-defined numerical method for problems for which
derivatives may not be known.
• The Nelder–Mead technique is a heuristic search method that was
proposed by John Nelder & Roger Mead (1965) for minimizing an
objective function in a many-dimensional space.
131
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 132
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
133
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 134
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
135
Basic movements
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
National Vegetable Research Station
136
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
;-)
137
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 138
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
2
139
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Genetic Algorithm (GA)
• The original motivation for the GA approach was a biological analogy. In the
selective breeding of plants or animals, for example, offspring are sought
that have certain desirable characteristics, characteristics that are
determined at the genetic level by the way the parents’ chromosomes
combine. In the case of GAs, a population of strings is used, i.e.
chromosomes.
• The recombination of strings is carried out using analogies of genetic
crossover and mutation, and the search is guided by the results of evaluating
the objective function f for each string in the population.
• Based on this evaluation, strings that have higher fitness (i.e., represent
better solutions) can be identified, and these are given more opportunity to
breed.
140
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023

15.
Terminology
141
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 142
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
143
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Coding
• One of the distinctive features of the GA approach is to allow the
separation of the representation of the problem from the actual
variables in which it was originally formulated.
• In line with biological usage of the terms, it has become customary
to distinguish the ‘genotype’—the encoded representation of the
variables, from the ‘phenotype’—the set of variables themselves.
144
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Translation
Genotype space = {0,1}L
(mappa)
Phenotype space
(territorio)
Encoding
(representation)
Decoding
(inverse representation)
01101001
01001001
10010010
10010001
145
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 146
Esempio: numero intero fra -7 e +7
Example
147
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 148
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Mating, Mutation, Selection
149
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
One or Two
150
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023

16.
IN ANOTHER (INDIRECT) WAY:
OPTIMALITY CRITERIA
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 151
Optimality Criteria
152
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
153
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 154
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
155
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 156
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
8. Constructive approach
• Insight in a structural problem
• Simple observations
9. Algorithms
• Direct way: basic aspects
• Surrogate
• Not so basic aspects
• Heuristics
• In another (Indirect) way:
optimality criteria
10.Levels in action
• Sizing
• Morphology
• Topology
• Generative
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 157
Index Part II
8. Constructive approach
• Insight in a structural problem
• Simple observations
9. Algorithms
• Direct way: basic aspects
• Surrogate
• Not so basic aspects
• Heuristics
• In another (Indirect) way:
optimality criteria
LEVELS IN ACTION
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 158
10
LEVELS IN ACTION
STRUCTURAL DESIGN AND OPTIMIZATION 2023
http://carat.st.bv.tum.de/caratuserswiki/index.php/Users:Structural_Optimization/General_Formulation
Optimization Levels
Micro-level:
local size of the sections,
i.e. thickness, area,
inertia, … (Detailed
Geometry)
Meso-level:
form of the structural
element or structural part
(substructure), i.e. main
longitudinal axis, curvature,
profile, … (Global Geometry)
Macro-level:
connections of the
different structural
parts (Load Path)
159
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
SIZING
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 160

17.
161
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Fully Stressed Design (FSD)
162
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
163
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Strutture isostatiche / iperstatiche
• Nelle strutture isostatiche il regime statico ovvero lo stato di sforzo
è determinato unicamente dalle condizioni di equilibrio (tra l’altro,
considerando piccoli spostamenti, il regime statico non è
influenzato dalle non linearità di materiale eventualmente
presenti).
• Nelle strutture iperstatiche, il regime statico ovvero la distribuzione
delle sollecitazioni e degli sforzi dipende dalla distribuzione delle
rigidezze, considerando che parti strutturali più rigide attirano
maggiori sollecitazioni e sforzi.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 164
FSD in action
165
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 166
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
167
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 168
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
169
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Solution that satisfies everything
[ ]
i
i
Design a
a max
4
,...
1
=
=
170
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023

18.
Industrial α - sections
171
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
A / W for HEB for α = h
A = 9E-13x6
- 3E-09x5
+ 5E-06x4
- 0,0036x3
+ 1,2509x2
- 139x + 7185,3
W = 1E-11x6
- 9E-08x5
+ 0,0002x4
- 0,2162x3
+ 113,67x2
- 17128x + 881393
0
2000000
4000000
6000000
8000000
10000000
12000000
14000000
0 200 400 600 800 1000 1200
A
W
Poly. (A)
Poly. (W)
172
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
IPE HEB
173
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Nota
• Con tale tecnica, si ottiene un dimensionamento che sfrutta a
pieno la capacità portante della sezione.
• Il progetto è basato quindi sul raggiungimento del requisito di
resistenza: un elemento strutturale e la struttura nel complesso
devono però soddisfare a differenti altri requisiti.
• È possibile considerare indirettamente questi altri aspetti anche
con il FSD: basta agire sui valori dei limiti tensionali o sui valori dei
moltiplicatori αmax ed αmin per dimensionare l’elemento con
riferimento ad altri aspetti che non siano la sola resistenza.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 174
175
175
Taglio / Instabilità
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 176
Es.
177
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 178
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
179
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 180
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023

19.
181
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 182
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
183
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 184
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
185
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 186
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
187
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
MORPHOLOGY
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 188
189
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 190
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023

20.
191
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 192
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
193
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 194
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
195
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 196
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Geometry Parameter Based Optimization
197
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Non-Parametric Optimization
198
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Hybrid optimization
199
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 200
200
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023

21.
Michell
201
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 202
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
203
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 204
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
205
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 206
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
207
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
TOPOLOGY
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 208
209
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 210
210
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023

22.
211
211
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 212
morfologica
topologica
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 213 214
Es.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
215
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 216
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
a b
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 217
Es. a
29-Jan-23 218
STRUCTURAL DESIGN AND OPTIMIZATION 2023
b
29-Jan-23 219
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 220

23.
221
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 222
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 223 224
STRUCTURAL DESIGN AND OPTIMIZATION
2023
29-Jan-23
Mesolivello
-
morfologico
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 225 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 226
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 227 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 228
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 229 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 230

24.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 231 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 232
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 233 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 234
STRUCTURAL DESIGN AND OPTIMIZATION
2023
29-Jan-23 235 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 236
237
STRUCTURAL DESIGN AND OPTIMIZATION
2023
Fundamental steps of the BG evolutionary process
29-Jan-23 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 238
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 239 240
STRUCTURAL DESIGN AND OPTIMIZATION
2023
240
29-Jan-23

25.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 241
Macrolivello
-
topologico
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 242
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 243 244
STRUCTURAL DESIGN AND OPTIMIZATION
2023
29-Jan-23
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 245 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 246
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 247 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 248
STRUCTURAL DESIGN AND OPTIMIZATION
2023
29-Jan-23 249 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 250

26.
STRUCTURAL DESIGN AND OPTIMIZATION
2023
29-Jan-23 251 STRUCTURAL DESIGN AND OPTIMIZATION
2023
29-Jan-23 252
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 253 STRUCTURAL DESIGN AND OPTIMIZATION
2023
29-Jan-23 254
STRUCTURAL DESIGN AND OPTIMIZATION
2023
29-Jan-23 255
Maillart’s Bridges
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 256
STRUCTURAL DESIGN AND OPTIMIZATION 2023 257
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 258
29-Jan-23
STRUCTURAL DESIGN AND OPTIMIZATION 2023 259
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 260
29-Jan-23

27.
STRUCTURAL DESIGN AND OPTIMIZATION 2023 261
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 262
29-Jan-23
STRUCTURAL DESIGN AND OPTIMIZATION 2023 263
29-Jan-23
Maillart
29-Jan-23 264
STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 265
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 266
STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 267
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 268
STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 269
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Ponti Maillart
29-Jan-23 270
STRUCTURAL DESIGN AND OPTIMIZATION 2023

28.
SHORTCUTS: DISCRETE MODELS
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 271 29-Jan-23 272
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Nb: vhange in topology
Morphology Optimization via OC
273
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 274
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
275
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 276
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
277
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Es.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 278
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 279 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 280

29.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 281
1° Step
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 282
2° Step
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 283 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 284
29-Jan-23 285
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 286
STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 287
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 288
STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 289
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 290

30.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 291 29-Jan-23 292
STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 293
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 294
STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 295 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 296
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 297 298
STRUCTURAL DESIGN AND OPTIMIZATION
2023
298
Smoothing / Streamlining
29-Jan-23
299
STRUCTURAL DESIGN AND OPTIMIZATION
2023
299
29-Jan-23
Design Process
300
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023

31.
Filters
301
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 302
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
303
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 304
STRUCTURAL DESIGN AND OPTIMIZATION
2023
Engineering Design Phases
29-Jan-23
Engineering …
• Minimum / maximum thicknesses
• Minimum / maximum lengths
•Symmetries
•Industrialized elements / components
•Manufacturing Procedures
(forging, bending, weldability, ...)
• Constructability
•Maintenability
•Inspectability
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 305
REFINED DESIGN
29-Jan-23 306
STRUCTURAL DESIGN AND OPTIMIZATION 2023
PROBLEM
29-Jan-23 307
STRUCTURAL DESIGN AND OPTIMIZATION 2023
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Meccanismo a cursore: 1a fase, aperto
29-Jan-23 308
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Meccanismo a cursore: 2a fase, chiuso
29-Jan-23 309
STRUCTURAL DESIGN AND OPTIMIZATION 2023
PORTATA MENSOLA
• La stragrande maggioranza dei tegoli (più dell’80% del
mercato USA) necessitano di una mensola con
capacità portante ULTIMA (UL) intorno ai 70 Kips.
• Dalle analisi siamo convinti che sarà possibile ridurre,
almeno in parte, il peso della mensola. In ogni caso il
peso complessivo della mensola non potrà superare i
7 Kg.
• Note:
• 70 Kips ULS = 70 x 4.45 kN = 312 kN = 31.2 t
• 70 / 2.5 = 28 Kips -> 312/2.5 = 125 kN = 12.5 t
29-Jan-23 310
STRUCTURAL DESIGN AND OPTIMIZATION 2023

32.
29-Jan-23 311
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 312
STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 313
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 314
STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 315
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 316
STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 317
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 318
STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 319
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 320
STRUCTURAL DESIGN AND OPTIMIZATION 2023

33.
29-Jan-23 321
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 322
STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 323
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 324
STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 325
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 326
STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 327
STRUCTURAL DESIGN AND OPTIMIZATION 2023
1.0 1.6 0.6
ANCHORAGEFORCE
SHEAR
(SUPPORTREACTION)
RIGHT END REACTION
29-Jan-23 328
STRUCTURAL DESIGN AND OPTIMIZATION 2023
1.0 1.6 0.6
ANCHORAGEFORCE
SHEAR
(SUPPORTREACTION)
RIGHT END REACTION
29-Jan-23 329
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Classe di resistenza acciaio
• Si è deciso di adottare per la forgiatura della mensola, acciaio tipo
S460M (ASTM 913 Grade 65) il cui valore di snervamento è 460
N/mm2 ed è particolarmente tenace e resiliente anche a basse
temperature.
• Il forgiatore ha già confermato la disponibilità ad usare questo acciaio.
29-Jan-23 330
STRUCTURAL DESIGN AND OPTIMIZATION 2023

34.
29-Jan-23 331
STRUCTURAL DESIGN AND OPTIMIZATION 2023
1.0 1.6 0.6
ANCHORAGE FORCE
SHEAR
(SUPPORT REACTION)
RIGHT END REACTION
29-Jan-23 332
STRUCTURAL DESIGN AND OPTIMIZATION 2023
12/20/2012 333
Limit
Stat
e
λ Shear
(slice 1.9685
inch)
Anchorage
(slice
1.9685
inch)
Right end
(slice
1.9685
inch)
Slice 0.3937
inch
(model)
Slice 3.1496
inch
(suggested)
kN Kips kN Kips kN Kips kN Kips kN Kips
SLS 1.0 120 26.98 190 42.71 72 16.19 24 5.40 192 43.16
ULS 1.5 180 40.47 285 64.07 108 24.28 36 8.09 288 64.74
SILS 1.9 230 51.71 365 82.06 139 31.25 45 10.12 365 82.06
1.0 1.6 0.6
ANCHORAGE FORCE
SHEAR
(SUPPORT REACTION)
RIGHT END REACTION
29-Jan-23 333
STRUCTURAL DESIGN AND OPTIMIZATION 2023
BASIC ANALYSIS
29-Jan-23 334
STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 335
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Comportamento Stringer&Panel
29-Jan-23 336
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Airframe Stringer & Panel
29-Jan-23 337
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Stringer Panel Method (SPM)
29-Jan-23 338
STRUCTURAL DESIGN AND OPTIMIZATION 2023
STRINGERS
29-Jan-23 339
STRUCTURAL DESIGN AND OPTIMIZATION 2023
STRINGERS PROPERTIES
29-Jan-23 340
STRUCTURAL DESIGN AND OPTIMIZATION 2023

35.
CONNECTION PROPERTIES
29-Jan-23 341
STRUCTURAL DESIGN AND OPTIMIZATION 2023
PANELS
29-Jan-23 342
STRUCTURAL DESIGN AND OPTIMIZATION 2023
PANELS PROPERTIES
29-Jan-23 343
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 344
STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 345
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 346
STRUCTURAL DESIGN AND OPTIMIZATION 2023
SWL elastic behavior
29-Jan-23 347
STRUCTURAL DESIGN AND OPTIMIZATION 2023
SWL elastic behavior
29-Jan-23 348
STRUCTURAL DESIGN AND OPTIMIZATION 2023
USL elastic behavior
29-Jan-23 349
STRUCTURAL DESIGN AND OPTIMIZATION 2023
USL elastic behavior
29-Jan-23 350
STRUCTURAL DESIGN AND OPTIMIZATION 2023

36.
USL elasto-plastic behavior
29-Jan-23 351
STRUCTURAL DESIGN AND OPTIMIZATION 2023
USL elasto-plastic behavior
29-Jan-23 352
STRUCTURAL DESIGN AND OPTIMIZATION 2023
USL elasto-plastic behavior
29-Jan-23 353
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 354
STRUCTURAL DESIGN AND OPTIMIZATION 2023
HOLES
29-Jan-23 355
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 356
STRUCTURAL DESIGN AND OPTIMIZATION 2023
correnti
fori
29-Jan-23 357
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Forgiatura
29-Jan-23 358
STRUCTURAL DESIGN AND OPTIMIZATION 2023
COMPARISON
ANSYS - ABAQUS
29-Jan-23 359
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Ansys
29-Jan-23 360
STRUCTURAL DESIGN AND OPTIMIZATION 2023

37.
Ansys
Stato Limite di Esercizio Richiesto F = 120 KN
Total mechanical strain intensity
29-Jan-23 361
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Ansys
Stato Limite Ultimo Richiesto F=180 KN
Total mechanical strain intensity
29-Jan-23 362
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Ansys
Stato Limite di Collasso Richiesto F=230 KN
Total mechanical strain intensity
29-Jan-23 363
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Ansys
Stato Limite di Collasso Effettivo F = 260 KN
Total mechanical strain intensity
29-Jan-23 364
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Abaqus
29-Jan-23 365
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Abaqus
Stato Limite di Esercizio Richiesto F = 120 KN
29-Jan-23 366
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Abaqus
Stato Limite di Esercizio Effettivo F = 170 KN
29-Jan-23 367
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Abaqus
Stato Limite Ultimo Richiesto F=180 KN
29-Jan-23 368
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Abaqus
Stato Limite Ultimo Effettivo F = 195 KN
29-Jan-23 369
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Abaqus
Stato Limite di Collasso Richiesto F=230 KN
29-Jan-23 370
STRUCTURAL DESIGN AND OPTIMIZATION 2023

38.
Abaqus
Stato Limite di Collasso Effettivo F = 275 KN
29-Jan-23 371
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Ansys Vs Abaqus
29-Jan-23 372
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Abaqus
Stato Limite di Esercizio Richiesto F = 120 KN
Ansys
Stato Limite di Esercizio Richiesto F = 120 KN
29-Jan-23 373
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Abaqus
Stato Limite Ultimo Richiesto F=180 KN
Ansys
Stato Limite Ultimo Richiesto F=180 KN
29-Jan-23 374
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Abaqus
Stato Limite di Collasso Richiesto F=230 KN
Ansys
Stato Limite di Collasso Richiesto F=230 KN
29-Jan-23 375
STRUCTURAL DESIGN AND OPTIMIZATION 2023
PUSHOVER
0
50
100
150
200
250
300
350
0 5 10 15
Force
[KN]
Vert_Displ [mm]
Abaqus_ottimizzata (3D model) Ansys_Ottimizzata (2D model)
29-Jan-23 376
STRUCTURAL DESIGN AND OPTIMIZATION 2023
REFINED DESIGN
29-Jan-23 377
STRUCTURAL DESIGN AND OPTIMIZATION 2023
REFINED DESIGN
29-Jan-23 378
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Mesh
Str
Str
Str
Str
Str
o
Str
Str
Str
Str
Str
N
o
o N
N
GER
29-Jan-23 379
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Mesh
Str
Str
Str
Str
Str
o
Str
Str
Str
Str
Str
N
o
o N
N
GER
29-Jan-23 380
STRUCTURAL DESIGN AND OPTIMIZATION 2023

39.
λ=1.0
29-Jan-23 381
STRUCTURAL DESIGN AND OPTIMIZATION 2023
λ=1.5
29-Jan-23 382
STRUCTURAL DESIGN AND OPTIMIZATION 2023
λ=1.9
29-Jan-23 383
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Mesh + Concrete Block
29-Jan-23 384
STRUCTURAL DESIGN AND OPTIMIZATION 2023
λ=1.0 – 120 kN – 28 Kips
29-Jan-23 385
STRUCTURAL DESIGN AND OPTIMIZATION 2023
λ=1.5 – 180 kN – 40 Kips
29-Jan-23 386
STRUCTURAL DESIGN AND OPTIMIZATION 2023
λ=1.9 – 230 kN – 52 Kips
29-Jan-23 387
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Concrete Block - λ=1.0
388
29-Jan-23 388
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Concrete Block - λ=1.5
389
29-Jan-23 389
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Concrete Block - λ=1.9
390
29-Jan-23 390
STRUCTURAL DESIGN AND OPTIMIZATION 2023

40.
Structural Response
λ=1.9 – 230 kN – 52 Kips
λ=1.5 – 180 kN – 40 Kips
λ=1.0 – 120 kN – 28 Kips
29-Jan-23 391
STRUCTURAL DESIGN AND OPTIMIZATION 2023
UNDER FIRE
(ISO Fire - Steel Temperature)
29-Jan-23 392
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Steel mechanical properties degradation
T
<=100°C
200°C
400°C
600°C
800°C
500°C
2%
e
20%
0.2% 15%
s
fyk
29-Jan-23 393
STRUCTURAL DESIGN AND OPTIMIZATION 2023
0
200
400
600
800
1000
0 10 20 30 40 50 60
ISO 834
θ steel
ISO Fire - Steel Temperature
29-Jan-23 394
STRUCTURAL DESIGN AND OPTIMIZATION 2023
ANSYS
ABAQUS
PANEL STRESS, t= 0 sec, T= 20 °C, Yield stress 450 N/mm2
29-Jan-23 395
STRUCTURAL DESIGN AND OPTIMIZATION 2023
ANSYS
ABAQUS
PANEL STRESS, t= 565 sec, T= 576 °C, Yield stress 245 N/mm2
29-Jan-23 396
STRUCTURAL DESIGN AND OPTIMIZATION 2023
PANEL STRESS, t= 650 sec, T= 618 °C, Yield stress 192 N/mm2
ANSYS
ABAQUS
29-Jan-23 397
STRUCTURAL DESIGN AND OPTIMIZATION 2023
PANEL STRESS, t= 730 sec, T= 651 °C, Yield stress 156 N/mm2
ANSYS
ABAQUS
29-Jan-23 398
STRUCTURAL DESIGN AND OPTIMIZATION 2023
PANEL STRESS, t= 770 sec, T= 665 °C, Yield stress 141 N/mm2
ANSYS
ABAQUS
29-Jan-23 399
STRUCTURAL DESIGN AND OPTIMIZATION 2023
0
2
4
6
8
10
12
14
0 200 400 600 800
displ
[mm]
TEMP [°C]
Ansys
Abaqus
Structural Response (1)
29-Jan-23 400
STRUCTURAL DESIGN AND OPTIMIZATION 2023

41.
0
2
4
6
8
10
12
0 5 10 15
displ
[mm]
Time [min]
Ansys
Abaqus
Structural Response (2)
29-Jan-23 401
STRUCTURAL DESIGN AND OPTIMIZATION 2023
0
200
400
600
800
1000
1200
0 20 40 60 80 100 120
ISO 834
Acciaio non protetto
pittura intumescente
schiuma PROMAFOAM d=7mm
Gesso
Time [min]
TEMP
[°C]
Protective Measures
29-Jan-23 402
STRUCTURAL DESIGN AND OPTIMIZATION 2023
EXPERIMENTAL RESULTS
29-Jan-23 403
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 404
STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 405
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 406
STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 407
STRUCTURAL DESIGN AND OPTIMIZATION 2023
Mensola ottimizzata peso ≈ 5.3 kg
Roma, 03 dicembre 2012
29-Jan-23 408
STRUCTURAL DESIGN AND OPTIMIZATION 2023
2D
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 409
STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 410

42.
411
3D
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 412
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 413 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 414
415
415
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 416
416
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
Vincoli funzionali
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 417 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 418
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 419 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 420

43.
421
421
Es.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
http://www.dezeen.com/2013/08/22/qatar-national-convention-centre-by-arata-isozaki/
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 422
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 423 424
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
425
425
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 426
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 427 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 428
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 429 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 430

44.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 431 432
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
433
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 434
GENERATIVE
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 435 436
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
437
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 438
Script
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 439 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 440

45.
441
441
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 442
443
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 444
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 445
http://thecreatorsproject.vice.com/blog/cgi-crowd-simulation-battle
446
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 447
8. Constructive approach
• Insight in a structural problem
• Simple observations
9. Algorithms
• Direct way: basic aspects
• Surrogate
• Not so basic aspects
• Heuristics
• In another (indirect) way:
optimality criteria
10.Levels I action
• Sizing
• Morphology
• Topology
• Generative
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 448
Index Part II
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 449 29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 450

46.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 451
Abstract
• Structural engineering can nowadays make use of very remarkable computational
tools. This availability can lead to affirm that the entire process of designing and
verifying the quality of a structure can be automated.
• Paradoxically, the opposite is true: powerful tools require deep reflections on what
are the bases of structural design in order to consciously address the procedures
of representation and optimization available today.
• In this only in this way, that optimization can represent an effective fundamental
component of structural design, in order to try to maximize the performance of
the structures and their sustainability.
• In order to obtain a correct optimization, it is therefore necessary to examine the
roots of the design, to understand its meanings and evaluate the limits of the
different numerical implementations.
• The lessons of the course will develop the concepts underlying structural
optimization while presenting specific significant applications
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 452
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 453
• Monday 30 January
15.00-18.00 (3 hours)
• Prof. Franco Bontempi
• Basis of structural design
• The art of structural engineering. The
principles of design. The creative process.
Structural concept. Design context and
structural requirements. Structural values.
Design by evolution and innovation.
Integration and specialization. Path of
loads. Structural schemes and their limits.
Structural analysis.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 454
DAY 1
• D. Billington, The Tower and the Bridge: The New Art of
Structural Engineering
• E. S. Ferguson, Engineering and the Mind’s Eye.
• H. Simon, The Science of Artificial.
• G. Madhavan, Come pensano gli ingegneri. Intelligenze
applicate.
• B. Munari, Da cosa nasce cosa. Appunti per una
metodologia progettuale.
• P. L. Nervi, Scienza o arte del costruire?
• E. Torroja, La concezione Strutturale.
• L.E. Robertson, The Structure of Design.
• W. Lidwell, K. Holden, J. Butler, Universal Principle of Design.
• U. Kirsch, Structural Optimization. Fundamentals and
Applications.
• S. Adriaenssens, P. Block, D. Veenendaal, C.Williams. Shell
Structures for Architecture: Form Finding and Optimization.
• M. Sarkisian, Designing Tall Buildings: Structure as
Architecture.
• Tuesday 31 January
10.00-13.00 (3 hours)
• Prof. Franco Bontempi
• Qualitative and quantitative aspects of
structural optimization
• Setting up the structural problem.
Uncertainties and undefinitions. Limited
rationality and partial knowledge.
Structural modeling. Solution of the
structural problem and its critical
judgment. Naïve setting of optimization
problems. Optimization algorithms.
Stochastic aspects. Heuristic approaches.
Discrete structural schemes.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 455
DAY 2
• Tuesday 31 January
15.00-18.00 (3 hours)
• Dr. Valentina Tomei
• Optimization strategies for the design of
gridshell type structures
• Notes on the types of structural optimization
and on the single-objective and multi-
objective optimization algorithms of an
evolutionary type. Notes on strategies for
finding the optimal shape: form-finding.
Gridshell type structures. The role of form in
gridshells. The role of structural optimization
in gridshell design: examples of design
strategies.
• Wednesday 1st February
15.00-18.00 (3 hours)
• Prof. Elena Mele
• Optimization of structures for tall
buildings
• Behavior of tall buildings, "premium for
height" and structural types. Notes on the
evolution of the structural design of tall
buildings and recent trends: the search for
efficiency and the role of robustness.
Diagrid structures and structural patterns:
sectional and topological optimization.
Patterns inspired by isostatic lines.
Generative design and shape grammar.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 456
DAY 3
• Wednesday 1st February
10.00-13.00 (3 hours)
• Prof. Francesco Petrini
• Optimization in the performance design of
buildings under wind action and seismic
action
• Application of optimization methods to real
problems. Performance-based design: general
aspects and specific characteristics.
Optimization of devices for the control of
vibrations of tall buildings under the action of
the wind. Risk-based design of reinforced
concrete frames in seismic zone with
development of an optimization procedure
based on the gradient method.
29-Jan-23 STRUCTURAL DESIGN AND OPTIMIZATION 2023 457
DAY 4
• Thursday 2nd February
10.00-13.00 (3 hours)
• Dr. Innocenzo Becci
• Seismic recovery of prefabricated buildings
with the use of dissipation systems and
decoupling systems
• With a technical practice setting, the
presentation concerns the seismic
improvement design approach on
prefabricated structures with the use of
mechanical connection and dissipation
devices. For the typological conception of the
mechanisms and for the materials used in the
systems, the selection criteria and the
experiences of experimental feedback which
have made it possible to validate the expected
operating principles will be exposed.
• Thursday 2nd February
15.00-18.00 (3 hours)
• Prof. Arch. Patrizia Trovalusci
• The construction of form in architectural
works: critical issues and advantages of
the mathematical/numerical approach
• The lesson presents, explores and
discusses mainly qualitative aspects
concerning works of architecture and is
accompanied by some examples of study
addressed in some degree theses (which
are available at this link:
https://sites.google.com/a/uniroma1.it/pa
triziatrovalusci/tesi-di-laurea/tesi-di-
laurea-sdc)
Structural Design and Optimization
Part II – V edition, 2023
Prof. Ing. Franco Bontempi
Docente di TEORIA E PROGETTO DI PONTI – GESTIONE DI PONTI E GRANDI STRUTTURE
Facoltà di Ingegneria Civile e Industriale
Università degli Studi di Roma La Sapienza
franco.bontempi@uniroma1.it