Master CYTEA – Domenico LAURIOLA

Master CYTEA – Domenico LAURIOLA Combining Efficiency and Aesthetics

Through The Integration Of Structural Topology Optimization in

Degree of Master of Science and Building Technologies in Architecture at Technical University of Cartagena

Domenico Lauriola

Faculty of Architecture and Building Engineer. Technical University of Cartagena

Master CYTEA – Domenico LAURIOLA

Master CYTEA – Domenico LAURIOLA Technical University of Cartagena Department of Applied Mathematics and Statistics Department of Structures and Construction

Director

Mathieu Kessler Department of Applied Mathematics and Statistics

Co-Director

Jesús Martínez Frutos Department of Structures and Construction

Master CYTEA – Domenico LAURIOLA

Master CYTEA – Domenico LAURIOLA

Abstract

The eternal fight of the functionality and aesthetic has written a large portion of the construction history. Engineer versus architect. The modernity has accentuated the problem because of the entrance of more variables: money and velocity. But is there any way to go out from the fights and approach the contemporaneity?

Probably the best way to figure out this problem is to look to the duality of aesthetic and functionality into the nature. How the nature has solved this problem according to the thermodynamics’ and physic’ laws? is there any algorithm to simulate this process?

This works is going to try to find the better way to use the newest tools and the powerful computing calculation capacity to solve the eternal fight. To pick out the better work flow to generate a new architecture that has the capacity to merge the functionality aesthetic of the nature into a new way to design a building.

Master CYTEA – Domenico LAURIOLA

Master CYTEA – Domenico LAURIOLA

Table of Contents

Introduction ...... 0 1-1 Objective ...... 1 1-2 State of the art of optimization techniques in architecture and its controversial opinion...... 1 1-3 BIM, software interoperability and optimization problems ...... 6 Combining aesthetic and structural efficiency ...... 8 2-1 Antonio Gaudí ...... 8 2-1-1 The Method ...... 8 2-1-2 Gaudí and his approach to the design problem ...... 12 2-1-3 Sagrada Familia ...... 15 2-2 ...... 21 2-2-1 Palace of Labour ...... 25 2-2-2 Burgo Paper Mill ...... 28 2-2-3 Nervi’s method for evaluating isostatics ...... 31 2-3 Felix Candela ...... 35 2-3-1 Optimal concrete shells ...... 39 Connecting architecture and engineering through structural Topology Optimization ...... 42 3-1 Topology Optimization Formulation ...... 42 3-1-1 Problem statement ...... 42 3-1-2 Structural Optimization ...... 44 3-1-3 Sizing Optimization ...... 44 3-1-4 Shape Optimization ...... 45 3-1-5 Topology Optimization ...... 45 3-1-6 Evolutionary Structural Optimization (ESO) ...... 53 3-1-7 Iso-Eso Optimization ...... 55 3-1-8 Tree-Inspired Optimization ...... 60 Applications of topology optimization in architectural design ...... 67 4-1 A form finding tool for evolutionary topology optimization ...... 67 4-2 Tool validation through academic examples ...... 70

Master CYTEA – Domenico LAURIOLA 4-2-1 Fixed board bridge with uniform vertical force ...... 70 4-2-2 Optimum design topology with ESO method for traction and compression structures ...... 73 4-3 Applications to architectural design ...... 83 4-3-1 One column ribbed floor case ...... 83 4-3-2 Four columns ribbed floor case ...... 90 4-3-3 Computer-aided form finding and optimal design of branching structures – parking roof example ...... 97 4-3-4 Topology Optimization – Bridge Example ...... 104 Conclusions ...... 109 5-1 SWOT Analysis ...... 110 Bibliography ...... 113

Master CYTEA – Domenico LAURIOLA

Table of Figures

Figure 1 : Retaining walls of the Güell Park at Barcelona ...... 10 F