Design sensitivity plays a critical role in inverse and identification studies, as well as numerical optimization, and reliability analysis. Herein, we review the state of design sensitivity analysis as it applies to linear elliptic systems. Both first- and second-order sensitivities are derived as well as first-order sensitivities for symmetric positive definite eigenvalue systems. Although these results are not new, some of the derivations offer a different perspective than those previously presented. This article is meant as a tutorial, and as such, a simple two-degree-of-freedom spring system is employed to exemplify the sensitivity analyses. However, the concepts presented in this trivial example may be readily extended to compute sensitivities for complex systems via numerical techniques such as the finite element, boundary element, and finite difference methods.

Design sensitivity analysis: Overview and review

▪ AbstractThis paper is a short and nonexhaustive survey of some recent developments in optimal shape design (OSD) for fluids. OSD is an interesting field both mathematically and for industrial applications. Existence, sensitivity, and compatibility of discretizations are important theoretical issues. Efficient algorithmic implementations with low complexity are also critical. In this paper we discuss topological optimization, algorithmic differentiation, gradient smoothers, Computer Aided Design (CAD)-free platforms and shock differentiation; all these are applied to a multicriterion optimization for a supersonic business jet.

Shape optimization in fluid mechanics

The general problem of concern is to find the optimum shape of an elastic body, which requires minimizing an objective function subject to stress, displacement, frequency, and manufacturing constraints. The basic approach so far has been to choose a set of geometric design variables that define the shape of the structure. Typically the design variables have been chosen as coefficients of splines and polynomials, coordinates of ‘control’ nodes, and other geometric parameters. An automatic finite element discretization scheme that uses geometric entities such as lines, arcs, splines, and blending functions, is then used to relate changes in position of interior grid points in the finite element mesh to changes in the design variables. In this paper, a set of natural design variables is chosen as the design variables defining the shape. Specifically, the design variables are the magnitudes of a set of fictitious loads applied on the structure. The displacements produced by these fictitious loads, or natural shape functions, are added onto the initial mesh to obtain the new shape. Consequently, a linear relationship is established between changes in grid point locations and design variables through a finite element analysis. Plane elasticity problems are solved using the new approach. The quality of the finite element meshes produced and other salient features of the shape optimal design problem are discussed.

A shape optimization approach based on natural design variables and shape functions

This article introduces variable chromosome lengths (VCL) in the context of a genetic algorithm (GA). This concept is applied to structural topology optimization but is also suitable to a broader class of design problems. In traditional genetic algorithms, the chromosome length is determined a priori when the phenotype is encoded into the corresponding genotype. Subsequently, the chromosome length does not change. This approach does not effectively solve problems with large numbers of design variables in complex design spaces such as those encountered in structural topology optimization. We propose an alternative approach based on a progressive refinement strategy, where a GA starts with a short chromosome and first finds an ‘optimum’ solution in the simple design space. The ‘optimum’ solutions are then transferred to the following stages with longer chromosomes, while maintaining diversity in the population. Progressively refined solutions are obtained in subsequent stages. A strain energy filter is used in order to filter out inefficiently used design cells such as protrusions or isolated islands. The variable chromosome length genetic algorithm (VCL-GA) is applied to two structural topology optimization problems: a short cantilever and a bridge problem. The performance of the method is compared to a brute-force approach GA, which operates ab initio at the highest level of resolution.

http://strategic.mit.edu/docs/2_7_SMO_VCLGA.pdf

Variable chromosome length genetic algorithm for progressive refinement in topology optimization

A unified method for continuum shape design sensitivity analysis and optimal design of mechanical components is developed. A domain method of shape design sensitivity analysis that uses the material derivative concept of continuum mechanics is employed. For numerical implementation of shape optimal design, parameterization of the boundary shape of mechanical components is defined and illustrated using a Bezier surface. In shape design problems, nodal points of the finite element model move as the shape changes. A method of automatic regridding to account for shape change has been developed using a design velocity field in the physical domain that obeys the governing equilibrium equations of the elastic solid. For numerical implementation of the continuum shape design sensitivity analysis and automatic regridding, an established finite element analysis code is used. To demonstrate the feasibility of the method developed, shape design optimization of a main engine bearing cap is carried out as an example.

3‐D shape optimal design and automatic finite element regridding

Numerical Methods of Shape Optimal Design

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Jean Cea

Author Tools

Chat about Author

Papers

Numerical Methods of Shape Optimal Design