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in meeting the challenge of making a structurally integrate structural analysis capabilities into such. poor forms work in spite of their inefficiencies software It is critical that such analysis be fast or. Macdonald 2001 However this does not mean that ideally real time to allow for an interactive user. this is the best way forward This paper argues for experience This type of feature shows users how. and presents an alternate paradigm in which design changes will affect structural performance. structural considerations are integrated into the according to metrics such as required material. form making phase of the design process conceptual volume structural stiffness or estimated construction. design costs This has been implemented in a number of. applications both in research and practice but is, Existing Computational Design Tools limited by the speed of computational structural. Today s architecture and engineering practices make. widespread use of computational tools throughout the. Guidance Features,design process and currently available tools both. reflect and enforce existing design paradigms Hsu To shift engineering software from the existing. and Liu 2000 Wang et al 2002 analysis and verification focus tools for structural. design should include form guiding capabilities This. Geometry based Tools for Architects type of feature enables the software to suggest new. geometries to the user in order to improve the,Architecture tools starting with Computer Aided. structural performance of a design concept While the. Drafting programs in the 1980s allow users to,field of optimization offers insight into ways to. thoroughly document and more recently generate,achieve this there has been little progress in.

both conceptual and detailed designs An increasing. developing guidance based tools for conceptual, interest in complex geometry has led to powerful 3D. design both in research and practice To truly,modeling software which coupled with scripting. encourage integrated conceptual structural design, capabilities enables the development of impressively. through modern computational tools it is critical that. complex forms,methodologies that achieve this functionality be. further developed,Analysis based Tools for Engineers.

Computational tools for structural analysis mirror Optimization in Structural Design. architecture tools in their power and capacity for. complexity and yet also maintain existing design Structural optimization is a promising field with a. roles Finite element analysis or FEA programs are rich history but has nevertheless yet to make a. capable of determining stresses deflections and significant impact on structural design in practice. dynamic behavior for highly complicated geometry This section explains the development of structural. using very sophisticated techniques Recent optimization theory and discusses the reasons for its. developments focus on increased accuracy and speed disconnect with design. under a range of conditions However these tools are The history of structural optimization can be. of little use in conceptual design they require a traced back to Galileo Galilei 1564 1642 who in. geometry be provided to be analyzed and are 1638 determined the optimal shape of a cantilevered. incapable of assisting with geometry generation beam subjected to a point load at its free end. Again these tools relegate engineers to the tasks of Timoshenko 1953 Heyman 1998 By finding the. verifying the form and sizing the members thus parabolic profile as illustrated in Fig 2 Galileo. limiting or eliminating their involvement in showed that mathematics can be used to find forms. conceptual design that use material as efficiently as possible to support. a given load For many years since this has been the. Key Structural Design Tool Features goal of structural optimization. The emerging research area of computational,structural design tools seeks to bridge the gap. between these existing computational approaches, enabling a true integration of structural input during. conceptual design This paper identifies two key, types of features for such tools feedback and Figure 2 Drawings from Galileo s Dialogues. guidance Concerning Two New Sciences 1638 showing in a. an incorrect linearly varying solution for the optimal. Feedback Features shape of a cantilevered constant width beam. supporting a point load at its tip along with b the. A clear remedy for the lack of performance,correct parabolically varying solution Timoshenko. evaluation in geometry generation tools is to, Since Galileo scholars have solved a steady of problem is referred to as size optimization While.

stream of increasingly complex structural improvements since the 1960s have broadened the. optimization problems Wasiutynski and Brandt reach of structural optimization strategies the general. 1963 One of the most well known contributions disconnect between the goals and reality of structural. comes from Anthony G M Michell s work on optimization persist still today In short although. another cantilever problem almost three hundred structural optimization aims to generate new and. years after Galileo s original work Michell showed exciting forms most applications are limited to rather. how to find an optimal truss solution for the narrow problem spaces. point loaded cantilever problem and a few others in An important step forward in structural. his seminal 1904 paper The Limits of Economy of optimization was the development of shape. Material in Frame structures Like Galileo Michell optimization or the determination of overall. was looking for minimal material analytical solutions structural form as opposed to element sizes. for key canonical problems rather than offering a Vanderplaats 1982 Bennett and Botkin 1986 Haftka. general approach for optimization of any structure and Grandhi 1986 Most applications of this early. Timoshenko 1953 Heyman 1998 work were in structural design of components in the. A more general approach that resembles automotive and aerospace industries where an. methods in use today was developed in the 1960s improved part would be used hundreds or thousands. with critical work by Schmit 1960 A cohesive of times yielding extensive savings although there. overview of work since is given by Spillers and are also examples of shape optimization for trusses. MacBain 2009 In contrast with the analytical sometimes called geometry optimization Because it. methods of scholars like Galileo and Michell the deals with overall form shape optimization is more. new numerical methods attempted to find the relevant to conceptual design than size optimization. optimum by iterating through potential solutions in a The third type of structural optimization used. systematic way Kirsch 1981 While iterative today is topology optimization or the optimal. approaches were practically impossible in the days of connective arrangement of elements in a structure. manual calculation the newly developed computers developed numerically in the late 1980s Bends e. brought rapid calculations for large problems to and Kikuchi 1988 Rozvany 2001 Rozvany 2007. reality This type of optimization can also be integrated with. shape optimization and size optimization,Specific methods have been developed to. address each of the three classes of structural,optimization problems but in general they share a. common formulation described in the following,subsection. Optimization Problem Formulation,Formally structural optimization is a numerical. method of finding the best solution according to,mathematically formulated functional requirements.

or objectives while conforming to mathematically, formulated constraints The solution is expressed in. the form of numerical values for a design vector x. Figure 3 25 bar trussed tower with member cross which represents a list of design decisions to be made. sectional diameters and wall thicknesses chosen by. for example nodal positions material selections,an optimization algorithm Fox and Schmidt 1966. cross sections called design variables, Importantly structural optimization researchers The objective function f x is often a. in the 1960s referred to their discipline as structural calculation of the weight or volume of the structure. synthesis Schmit 1981 Vanderplaats 2010 such that a minimal weight structure can be found. revealing the early aspirations of the field and However this function can also consider stiffness. evoking ideas of design in its truest sense creating strain energy deflection or other quantitative goals. something new However the work actually dealt structural or otherwise The constraints g x 0 and. with choosing member cross sections for h x 0 and the variable bounds xi lb and xi ub. predetermined geometries and member restrict the solutions according to design or. configurations Fox and Schmit 1966 For example behavioral requirements More specifically design. Fig 3 shows a three dimensional truss tower with 25 constraints can represent geometric or spatial. elements whose cross sections were selected using a requirements constructability or fabrication. numerical weight minimization algorithm This type limitations or other functional considerations. Behavioral constraints set limitations on structural. behavior and include restrictions on performance practice tools that use optimization should be easy to. metrics like internal stresses deflections or buckling use integrated and strongly graphical. capacity Kirsch 1981, Together the design vector constraints Interactive Design Space Exploration. variable bounds and objective function define a,Given the issues with standard optimization in.

design space or solution space for a given problem. conceptual structural design it is necessary to look. The dimension of this space is given as one more,beyond the established approaches to find ways to. than the number of design variables to represent the. bring computational design guidance to conceptual,space of possible design vector values and their. design tools, resulting objective or performance values Structural. Interactive optimization addresses this issue in,design problems often have design spaces that are. a simple but compelling way the designer is allowed. large and complex although the exact nature of the. to interact with the computer algorithm in deciding. design space depends on the specifics of the problem. which designs to pursue in the iterative optimization. process The exact mechanics of the interaction,Limitations of Optimization in Design.

depend on the specific algorithm chosen In general. Despite the rich academic history of structural the interactive element allows the user to only. optimization it has had relatively little impact on partially formulate the design problem in a. structural engineering in practice Fundamentally this quantitative way and to use unformulated or newly. can be attributed to an inherent difference in goals discovered objectives and constraints to make design. between optimization and the design of buildings selections. While optimization is necessarily a convergent, process or one in which an iterative and systematic Interactive Evolutionary Algorithms. algorithm converges upon a single solution design is. Evolutionary algorithms are a general class of, decidedly divergent In design it is recognized that a. optimization strategies that use the principles of. variety of significantly different yet suitable solutions. Darwinian natural selection to grow and evolve,can be found from a single starting point. populations of designs They have the advantages of. Moreover the exercise of mathematically,being robust and well suited to complicated. formulating objectives and constraints is difficult or. engineering problems Because they incorporate,impossible in the design of buildings Many goals.

randomness they avoid getting stuck in local optima. and requirements are qualitative or even subjective. and can effectively hop around the design space in. such as visual impact spatial experience contextual. search of better solutions,fit and overall architectural value Since most. Furthermore because they work with,structural design cannot occur in the absence of. populations of candidate designs evolutionary,architectural goals this presents a significant. algorithms are especially useful in promoting design. diversity Unlike algorithms that focus on improving. In addition the design process for buildings is, singular solutions these algorithms improve a group. often one of discovery designers do not know all of. of alternative options as they iterate The general. their objectives and constraints at the beginning of. procedure is to randomly initialize a first generation. the process but develop them as they explore design. evaluate the fitness of each member of the generation. possibilities The designer s interaction with the, identify the top performers and use those to create a.

process of evaluation and iteration is key In contrast. subsequent generation by combining and mutating,standard optimization is a relatively rigid and. them In standard evolutionary algorithms the,automated process in which goals and requirements. process runs automatically until preset criteria are. must be enumerated completely at the start Unlike,reached and a single solution is present. From analysis to design A new computational strategy for structural creativity Caitlin Mueller and John Ochsendorf caitlinm mit edu jao mit edu Building Technology Program Massachusetts Institute of Technology United States Abstract Since the introduction of finite element analysis software in the 1970s structural engineers have

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