computational design of sustainable urban …...shells, membranes and spatial structures:...

USP-PU Strategic partnership 2014-2015

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Computational Design of Sustainable Urban Infrastructure

Sigrid Adriaenssens1 and Ruy Marcelo de Oliveira Pauletti2 1 Department of Civil and Environmental Engineering, Princeton University (PU) 2 Departamento de Engenharia de Estruturas e Geotecnica, Universidade de São Paulo (USP)

Overview of the field of study and general intellectual context for non-specialist audience

Energy consumption is a global strategic issue. With more than 50% of the human population living in

growing urban areas, improving building-energy efficiency is a major challenge. The building sector

accounts for approximately 40% of the world’s energy consumption and associated carbon dioxide (CO2)

emissions. According to the US Energy Information Administration, the US building sector uses

approximately 40% of the primary energy. Of this energy, 75% is provided by fossil fuels, largely due to

the energy required during construction phases. In Brazil, the building sector accounts for 45% of the

national energy consumption. Therefore, it is important to investigate strategies for the design of

urban infrastructure that will reduce energy consumption and C02 emissions.

By efficiently using materials required for construction, environmental and economic costs can be

reduced. Lightweight structures describe structural systems for architectural applications that use as

little material as possible to support the applied loads, therefore lowering costs. However, designing

lightweight structures, such as cable and shell structures, is a challenging task: the definition of their

initial equilibrium shape often requires the use of experimental or computational methods, widely

known as form-finding techniques. Our proposal focuses on a numerical method (form-finding and

analysis algorithm) which promotes the design of efficient lightweight structures, therefore

contributing to green engineering and sustainable design.

The $8 000 seed grant will be allocated to enable i) a three-day trip to USP for two PU faculty/research

members and ii) a five-day trip to PU of a USP faculty member. The trips will be of both educational and

research character. During these stays, we will give a short course on form-finding to graduate students

at both institutions. We intend to value our research collaboration with the writing of research

proposals (FAPESP, CNPq, FINEP, US NSF) and a journal publication. The trip to USP will also be

combined with presentation of the research carried out at PU at the “IASS-SLTE 2014 Symposium --

Shells, Membranes and Spatial Structures: Footprints”, organized by USP in Brasilia, from 15-19

September 2014. The theme of the Symposium, aimed at “improving our urban spaces, reducing our

ecological footprint” acknowledges the relevance of the research proposed in this application. The PU

faculty member has already been invited to be a member of the symposium’s international scientific

committee. In addition, we have just accepted the invitation to co-organize an invitation session on

recent advances in the form-finding method, dynamic relaxation, at the “Structural Membranes 2015”

conference, held in Barcelona. At this scientific meeting, we will jointly present and discuss our work

with other international experts in the field. Although no budget is requested in this proposal for this

last event, this co-organized session does underline our intent to develop a broader and long-term

partnership.


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Content of the proposal

1. Objectives, state of the art and research completed by the applicants

2. Global aspirations, long term programming and student engagement

3. Detailed plan of the initiative and milestones

4. Profile and interests of sponsoring departments

5. Funding contributions from sponsoring units and strategy for longer-term support

6. Concluding thoughts

7. Answers to Parts 1 and 3 of the first phase evaluation

8. References

1. Objectives, state of the art and research completed by the applicants

1.1. Objectives

This proposal promotes green engineering and sustainable design at PU and SPU through a joint effort

that focuses on the development of numerical methods for form-finding and analysis algorithms for

sustainable, lightweight structural systems. The objectives of this proposal are as follows:

1. Explore prospects for collaboration and translate them into research proposals;

2. Provide a short course on form-finding to PU and USP graduate students; and

3. Explore current research developments for a joint journal publication.

1.2. State of the art on form-finding and analysis based on the dynamic relaxation formulation

A challenge for architects and engineers in the design of structurally efficient systems is the generation

of good structural forms for a specific set of boundary conditions, a process known as form-finding [1].

In this proposal, we plan to focus on dynamic relaxation (DR), a well-established, explicit, numerical

analysis method used for the form-finding and analysis of highly non-linear structures [2]. The method

avoids stiffness-matrix calculations [3] and is thus computationally highly beneficial for the form-finding

and analysis of nonlinear structures. With its low computational cost, DR has high potential as a

computational design technique to generate a vast design space of structurally possible forms for

material-efficient structures. Therefore, DR presents a powerful tool for designers of the built

environment.

In DR, structures are modeled as a mesh of elements connecting nodes with masses. External loads are

applied to the nodes, while pre-stress can be applied in the structure through the definition of an initial

link length. The method relies on the concept that the static solution for a structure, subject to loading,

can be seen as the equilibrium state attained after the system undergoes damped vibration. For a

structural system discretized into nodes and elements, the motion of each node of a structure may be

traced step-by-step for small time increments, Δt, until, due to artificial damping, the entire system


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comes to rest in static equilibrium. In form-finding, the process begins from an arbitrarily specified

geometry, with the motion caused by imposing a stress or force specification in some or all of the

structural components. The method is also useful to solve highly non-linear static equilibrium problems,

when the process starts with a valid geometry (often a form-found one) and the motion is caused by

applying the corresponding loading. The governing equation for dynamic relaxation is:

(1)

where extF and intF are the external and internal forces at each node, respectively, M corresponds to

the nodal mass, and D to damping. Both mass M and damping D are fictitious parameters, optimized

for the stability and convergence of the method [4]. and are the acceleration and the velocity at each

node, respectively. In our proposal, kinetic damping is employed [5]. The motion of the structure is thus

traced. When a local peak in the total kinetic energy of the system is detected, all velocity components

are set to zero. Hence, the damping term in Equation (1) is abandoned. Expressing the acceleration in

finite difference form gives the velocity and the updated geometry for each node:

(2)

(3)

where vt+Δt/2 and vt-Δt/2 are the nodal velocities at times t+Δt/2 and t-Δt/2 respectively. xt+Δt is the nodal

position at time t+Δt. Equations (2) and (3) apply for all unconstrained nodes of the mesh in each

coordinate direction. A new geometry is thus obtained every time, allowing the estimation of new

internal forces Fint and the procedure to be repeated. Equilibrium and convergence are obtained when

the term in Equation (1) is sufficiently small.

Dynamic relaxation has been used as an explicit solution method for the static behavior of structures for

more than 40 years. The method was derived from an analogy related to tidal flow computations [6],

where equations of damped structural motion and the constitutive equations of elasticity substitute the

equations of fluid motion and continuity, respectively. Brew and Brotton [7] developed a formulation

that separated the equations for equilibrium and compatibility (motion) so that the formulation of an

overall stiffness matrix is not required, making it particularly advantageous for highly non-linear

structures especially when combined with kinetic damping [4]. Since 1965 [6], dynamic relaxation has

been significantly improved by Barnes [2], Papadrakakis [7], Wakefield [8], Topping [9] and more

recently by Wood [10] and Hand and Lee [11]. Although the convergence of the method was

significantly improved by the definition of a critical time step [7] and kinetic damping [4], no study has

found how to efficiently define the time step to optimize convergence. Our research objective is to

improve the performance of the dynamic relaxation method by developing an algorithm to correctly

define that time step. Preliminary results suggest that our research might achieve a major

improvement in the robustness of DR method, enhancing the computational design of lightweight

structures and promoting a future-oriented sustainable built environment.


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1.3. Research completed by the applicants

Previous work by the applicants has resulted in the development of the dynamic relaxation method with

novel elements and applications. The bending element, developed by the PU faculty member, deals with

moments and shear forces, when initially straight tubular members are deformed, using a spline type

formulation [12]. The scheme adopts a finite difference model of a continuous beam assuming that the

nodes of the element lay on a circular arc and that the bending stiffness is constant along the element.

The calculations and transformations required in the dynamic relaxation scheme for the bending

element are rather simple, with sets of three consecutive nodes being considered sequentially along the

entire transverse [12]. The torsion/bending element, further developed by the PU faculty member,

builds on the scheme developed for the bending element but extends its scope by accounting for torsion

and out-of-plane bending moments [13]. Transverse deformations are based only on the twists and

torsions related to a reduced torsion constant. The elements are particularly useful for modeling

lightweight structures such as grid shells that employ continuous tubular members, membranes in

which flexible battens are employed to give shape control or complex curved and tension active

structures. These algorithms directly lie at the basis of actually built material-efficient structures. Figure

1 shows the economic glass/steel grid shell over the courtyard of the Dutch Marine Museum (Ney and

Partners, Amsterdam, Netherlands) as well as the louvered shell prototype, designed to effectively

shade a user-defined area (Princeton, USA).

Figure 1: Urban infrastructure designed with PU developed DR algorithms: (left) cupola over Dutch Maritime

Museum (Amsterdam, Netherlands) and (right) small scale louvered shell prototype designed as shade for

Princeton.

Several applications of the DR method for the nonlinear analysis of cable and membrane structures have

also been presented by the USP faculty member in [14] and [15]. Extensions to the DR method to solve

equilibrium problems of membranes with sliding cables and for the determination of geodesic lines onto

membrane surfaces were presented in [16]. The versatility of the method to solve general non-linear

equilibrium problems, not necessarily of mechanical nature, was discussed in [17]. Figure 2 shows a

large pneumatic membrane, reinforced with sliding cables, built to cover the site of a nuclear power

plant. This system was modeled and analyzed according to the formulations presented in [16]. Figure 3

shows a mechanically pre-stressed membrane structure, an Amphitheatre for Children’s Rights (São Palo


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State, Brazil), for which the USP faculty member performed the form-finding and structural analysis

using in house developed coding of the DR method.

Figure 2: Urban infrastructure designed with USP developed DR algorithms: a pneumatic membrane reinforced

with sliding cables, realized to cover a nuclear plant site.

Figure 3: Urban infrastructure designed with USP developed DR algorithms: (top row) the Amphitheater for

Children Rights, in São Bernardo do Campo (São Palo State, Brazil); (bottom row left) numerical model; (right)

displacements (exaggerated), under wind loads.

Both PU and USP parties are at the forefront of research in the domain of DR. We strongly believe that

through our joint efforts we can make a transformative leap of knowledge by advancing the

development of the DR technique and improving the design of the urban environment.


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2. Global aspirations, long term programming and student engagement

2.1. Promotion of global aspirations and longer term programming of the home units

Our proposal incorporates the global aspirations of both our institutions: it increases the international

presence for USP and promotes a global view of academics at PU. To benefit USP, our proposal increases

international involvement through cooperative research as outlined in the guidelines of the USP

Provost’s Office for Research. For PU, our proposal reflects an effort to carry out cutting-edge research

and scholarship, internationally. Additionally, this effort builds a global-minded community at PU and

extends the PU’s strengths abroad. Prof. Pauletti, USP faculty member, is interested in establishing a

research group at USP that focuses exclusively on the form-finding and analysis of lightweight

structures. The Form-Finding Lab of Prof. Adriaenssens at PU combines state-of-the-art research on this

topic with academic excellence making it a valuable model for a new group at USP. These initiatives

reflect also the research agendas of our respective home units on the built environment.

In terms of long term programming, we hope that we will be able to leverage this initial seed grant to

attract longer-term research funding and student support to set up an exchange program for

undergraduate/graduate students and faculty/research members between USP and PU. Undergraduate

students will be given small research projects in accordance with both institutions (senior thesis,

independent research), while graduate students will be able to work on their existing research projects

(thesis) profit from the guidance of the hosting faculty member. Projects will have to be related directly

or indirectly to sustainable, lightweight structures and green engineering. We also plan to organize

workshops for students and related research members to present and discuss their projects, providing

valuable experience.

2.2. Engagement of Princeton/USP scholars and students in the partnership

The goal of our proposal is to convene and explore prospects for future collaboration and engagement

of PU/USP students; a direct budget is not foreseen for students in this specific proposal. The seed grant

will be allocated to enable the trips of two PU faculty/research members and one USP faculty member.

However, our trips will also have a direct educational impact. During our visits we will give a short

course on form-finding to graduate students at both institutions. While our immediate goal is the

establishment of a cooperative research program for future student exchange opportunities, current

students at both institutions will also profit from our respective stays.


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3. Detailed plan of the initiative and milestones

This proposal is based on two mutual visits of PU and USP faculty/research members. The detailed visit

schedule is given below:

Trip description Period

Trip to USP for two PU faculty/research members 10-12 September 2014*

Trip to PU of a USP faculty member 13-17 April 2015

* The trip to USP will be combined with PU participation at the 2014 IASS-SLTE Symposium on “Shells,

Membranes and Spatial Structures: Footprints”, which is organized by USP from September 15 to

September 19, 2014.

The milestones of this proposal include: (i) short courses on form-finding and analysis methods to

graduate PU and USP students, (ii) a journal paper and (iii) the submission of proposals to internal and

external funding institutions.

Milestone Period

Short courses on form-finding and analysis methods at USP 10-12 September 2014

Short courses on form-finding and analysis methods at PU 13-17 April 2015

Journal publication 2014 (to be defined)

Proposal submissions 2014-2015

4. Profile and interests of sponsoring departments

Our principal goal is to reduce energy consumption in the building sector through the promotion and

development of lightweight structures. Lightweight systems are material efficient which directly entails

lower environmental and economic cost, two direct consequences that are beneficial for society. The

search for an optimal and durable shape is a common recurring theme of our research groups. At PU,

the research group in the Form-Finding Lab (Prof. Adriaenssens) focuses on integrating safety, stability,

serviceability, as well as elegance, efficiency and economics in the structural design process. This focus

fits within the “sustainability of the built environment” research agenda of PU Civil and Environmental

Engineering (CEE) Department. This proposal reflects the interests of both the research group and CEE

department. At USP, the faculty member has focused on the development of numerical methods for the

analysis of cable, membranes and light structures while also offering courses in Graduate Programs on

Civil Engineering and Architecture of the University of São Paulo. Therefore, our research profiles are

clearly complementary. Our overarching research goal in this proposal is to improve the performance

of DR, a computational design method for lightweight sustainable structures and hence address some

of the most important issues regarding sustainability faced in the 21st century.


5. Funding contributions from sponsoring units and strategy for longer-term support

Our proposal is for a seed grant limited to a one year duration. However, our intention is to use the seed

funding to establish a long-term collaboration between the PU and USP.

The grant will be allocated to enable i) a three-day trip to USP for two PU faculty/research

members and ii) a five-day trip to PU of a USP faculty member to convene and explore prospects for

collaboration. Our hope is that, in a one-year period, we will be prepared to leverage longer-term

research funding and student support with the submission of small and larger proposals. These include

a three-year open grant to the USP-PU Strategic partnership, to other on-campus centers (Keller Center,

Andlinger Center for Energy and the Environment and Princeton Environmental Institute), to the

recently awarded Princeton-Mellon Architecture, Urbanism, and Humanities Initiative and to state and

government agencies such as FAPESP (São Paulo Research Foundation), CNPq (National Counsel of

Technological and Scientific Development, Brazil), FINEP (Agência Brasileira da Inovação) and US

National Science Foundation.

6. Concluding thoughts

The computational design method that we develop facilitates the design of lightweight, material-

efficient, structural systems. By reducing economic and environmental cost, these structures contribute

towards a more sustainable built environment. This design technique addresses global 21st century

societal questions involving fossil fuel depletion and global warming. This initial proposal aims to

establish a research collaboration between our institutions which (i) explores opportunities for research

proposals and translate them into proposals, (ii) offers a short course on form-finding to PU and USP

graduate students; and (iii) explores current in-house research developments for a joint journal

publication. Irrespective of these objectives, we have accepted an invitation to co-organize a scientific

session on recent advances in the DR method at the conference Structural Membranes 2015, Barcelona.

We hope that our partnership will allow us to leverage longer-term research funding and student

support for the initiative’s sustainability.

7. Answers to Parts 1 and 3 of the first phase evaluation

7.1. Answers to questions in Part 1

Does the proposal generate something new that would otherwise not exist?

Yes, our proposal supports an initiative which intends to establish a research collaboration between USP

and PU specifically focused on the computational design of sustainable urban infrastructure. The seed

grant will provide us the opportunity to convene and explore prospects for long-term collaboration and

establishing a state-of-the-art research center, modeled after the Form Finding Lab at PU, at the

Polytechnic School of USP.

We will promote this collaboration in research proposals submitted to the USP-PU Strategic

partnership, other on-campus centers and for state and government funding. The seed grant increases

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our chances for establishing a sustainable cooperative research program. However, this seed grant is not

limited to only the establishment of research collaboration. Current graduate students at both

institutions will also benefit from our initial proposal through a short course on form-finding techniques

at the occasion of our planned visits.

Does the funding effectively target the mobility of faculty and students back and forth

between Princeton and USP?

Yes, most of our budget is foreseen to increase the mobility of both PU and USP faculty. We would like

to fund (i) a three-day trip to USP for two PU faculty/research members and ii) a five-day trip to

Princeton of a USP faculty member). The trip to USP will be combined with PU participation at the 2014

IASS-SLTE Symposium, which is organized by USP from September 15 to September 19, 2014 in Brasilia.

Although there is no budget foreseen for student mobility, graduate students at both institutions will

benefit from the exchange through short courses.

Does the initiative direct the sponsoring unit to programmatic goals? If so, what are those

longer term goals?

Yes, our proposal will certainly seed development of ventures beyond the term of the grant itself since

its main objective is to support our initiative for the establishment of a long-term research collaboration.

Our initiative also directs the programmatic goals of our institutions. To benefit the USP, our proposal

increases international involvement through cooperative research following the guidelines of the USP

Provost’s Office for Research. For PU, our proposal reflects an effort to carry out important, cutting-edge

research and scholarship internationally. This effort will also help to build a global-minded community at

PU and extend PU’s strengths abroad. Both institutions have designated the “environment” as a

research axis, at a departmental and school level. Moreover, Prof. Pauletti would like to establish a

state-of-the-art research group in lightweight structures at USP. PU’s Form-Finding Lab is already an

established eminent research lab in this domain. Therefore, our collaboration will also benefit the

establishment of this novel group at USP.

The intellectual reasoning has to be excellent.

Prof. Pauletti (USP) has proposed extensions to the DR method for membrane structures with sliding

cables and for the determination of geodesic lines onto membrane surfaces [16]. He has also applied the

DR method for the nonlinear analysis of multiple cable and membrane structures [14-15]. Prof.

Adriaenssens (PU) has developed a bending element for DR that deals with moments and shear forces

[12] as well as a torsion/bending element that accounts for torsion and out-of-plane bending moments

[13]. Both elements are particularly useful for modeling lightweight structures such as grid shells that

employ continuous tubular members, membranes in which flexible battens are employed to give shape

control or complex curved and tension active structures. These developments directly lie at the basis of

actually built material-efficient structures.

Section 1 shows more extensively that the PU and USP partners are at the forefront of the field

developing the DR technique, as their previous work has resulted in the development of the dynamic


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relaxation method with novel elements and applications. A collaborative partnership would thus

enhance and amplify the impact that each institute can have.

What complementary resources are part of the package?

During the short stays, the USP faculty will have desk space as well as access to the Structural Models

Lab, a facility with several digital fabrication techniques (Laser cutter, 3D printer, etc.), to make physical

models that result from the DR form-finding design process. The USP faculty will also be introduced to

and have access to the Frank Powell archive, located in the CEE Department. This archive holds a rich

collection of articles, books, slides and construction drawings of prominent material-efficient structures.

The PU partners will have equivalent desk space at the Laboratory of Computational Mechanics of the

Polytechnic School of USP, well equipped to develop the numerical research envisioned in our proposal.

7.2. Answer to Part 3

Since your proposal is for more of a seed grant, our main suggestion is that you consider thinking

about ways in which you might submit a larger grant proposal in the future. This should include an

expansion of the numbers of participants, some ideas about longer-term collaboration, and possibly

institutionalizing the exchanges between your respective units. We hope that you will indicate to us

that developing broader partnerships is an aspiration of the seed grant.

Our proposal is our first effort towards the establishment of a research collaboration between USP and

PU on computational design of sustainable, urban infrastructure. The seed grant will be used to convene

and explore prospects for collaboration. Our hope is that, in a one-year period, we will be ready to

leverage longer-term research funding and student support with the submission of larger proposals.

These proposals would include a three-year open grant to the USP-PU Strategic partnership, to other on-

campus centers (Keller Center, Andlinger Center for Energy and the Environment, Princeton

Environmental Institute), to the recently awarded Princeton-Mellon Architecture, Urbanism, and

Humanities Initiative and to state and government agencies such as FAPESP (São Paulo Research

Foundation), CNPq (National Counsel of Technological and Scientific Development, Brazil), FINEP

(Agência Brasileira da Inovação) and US National Science Foundation. Therefore, we plan to develop a

framework that incorporates USP and PU students and faculty/research members to support our

exchange research program. The program will include (i) exchange of undergraduate and graduate

students, postdocs, faculty, with visits spanning from several days to a few months; (ii) joint courses on

computational design of sustainable urban infrastructure for undergraduate and graduate students; (iii)

a joint workshop for the promotion of our results and the discussion of research ideas that can deepen

and expand our collaboration; and (iv) a collaborative effort to establish a new Laboratory in USP, with a

large interaction with PU Form-Finding Lab.

The heart of our program will be the exchange of people and ideas between USP and PU. However, this

framework will also allow us to extend our research goals and include new participants from both our

institutions and other universities which can contribute to promoting a more sustainable built

environment.


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8. References

1. Veenendaal D., Block P. An overview and comparison of structural form finding methods for general networks.

International Journal of Solids and Structures, 49 (26): 3741-3753, 2012.

2. Barnes M.R. Form finding and analysis of tension structures by dynamic relaxation. International Journal of

Space Structures. 1999; 14:89-104.

3. Brew J.S., Brotton D.M. Non-linear structural analysis by dynamic relaxation. International Journal for

Numerical Methods in Engineering. 1971; 3(4):463-83.

4. Belytschko T.B., Hugues T.J.R. Computational methods for transient analysis. 1983.

5. Cundall P.A. Explicit finite-difference method in geomechanics. Numerical Methods in Geomechanics, ASCE,

1976.

6. Day A.S. An introduction to dynamic relaxation. 1965.

7. Papadrakakis E. Gradient and Relaxation non-linear techniques for the analysis of cable supported structures:

PhD thesis, City University, London; 1978.

8. Wakefield D. Dynamic relaxation analysis of pre-tensioned networks supported by compression arches: PhD

report, City University, London; 1980.

9. Topping B. The application of dynamic relaxation to the design of modular space structures: PhD thesis, The

City University, London; 1978.

10. Wood R. A simple technique for controlling element distortion in dynamic relaxation form-finding of tension

membranes. Computers & Structures 2002; 80(27–30):2115–20.

11. Han S, Lee K. A study of the stabilizing process of unstable structures by dynamic relaxation method.

Computers & Structures 2003; 81(17):1677–88.

12. Adriaenssens S., M.L. and Barnes M.R. (2001). Tensegrity spline beam and grid shell structures. Engineering

Structures, 23 (1), 29-36.

13. Barnes M., Adriaenssens S., Krupka M. (2013). A novel torsion/bending element for dynamic relaxation

modeling. Computers and Structures, 19 (1), 60–67.

14. Pauletti, R. M. O.; Guirardi, D. M.; Chivante, M. R. (2007) O MÉTODO DA RELAXAÇÃO DINÂMICA PARA A

ANÁLISE ESTÁTICA NÃO-LINEAR DE ESTRUTURAS DE CABOS E MEMBRANAS. CMNE/CILAMCE 2007, 2007,

Porto.

15. Pauletti, R. M. O.; Pappalardo JR, A.; Guirardi, D. M. (2008) “The method of dynamic relaxation for the static

nonlinear analysis of cable and membrane structures”. IASS-SLTE International Symposium 2008 - New

Materials and Technologies, New Design and Innovations A sustainable Approach to Architectural and

Structural Design, Acapulco, Mexico.

16. Pauletti, R.M.O., Guirardi, D.M. and Gouveia, S. (2009) “Modeling sliding cables and geodesic lines through

dynamic relaxation”. IASS International Symposium 2009 - Evolution and trends in design, analysis and

construction of shell and spatial structures”, Valence, Spain.

17. Pauletti, R. M. O. ; Guirardi, D. M. (2011) Direct Area Minimization through Dynamic Relaxation. Structural

Membranes 2011 - V International Conference on Textile Composites and Inflatable Structures, Barcelona,

Spain.

PROJECT SUMMARY (as it was cut off on the application form)

The building sector is one of the main energy consuming sectors in US and Brazil. By rethinking itsapproach towards design, this sector can substantially mitigate climate change. Our research focuses onthe form finding algorithms for lightweight structures with low environmental cost. We propose paperproposal writing activities, workshops and symposium participation.

computational design of sustainable urban …...shells, membranes and spatial structures:...

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