Structural shape optimization — a survey
Computer Methods in Applied Mechanics and Engineering
Boundary elements ten, an introduction
Boundary elements ten, an introduction
An Exact Probability Metric for Decision Tree Splitting and Stopping
Machine Learning
An Interior-Point Algorithm for Nonconvex Nonlinear Programming
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
A Survey of Shape Parameterization Techniques
A Survey of Shape Parameterization Techniques
A natural stress boundary integral equation for calculating the near boundary stress field
Computers and Structures
Reliability-based optimization of trusses with random parameters under dynamic loads
Computational Mechanics
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The shape optimization problem consists in looking for the geometry that minimizes an objective function, like mass or compliance, subject to mechanical constraints. The boundary element method (BEM) is used for the structural analysis. For linear elasticity problems, it needs only a mesh on the boundary of the structure. This characteristic makes the BEM a natural method for shape optimization, since only the boundary is needed to define the optimization problem and to carry out the structural analysis. The simultaneous analysis and design formulation (SAND) for structural optimization considers the state variables as unknowns of the optimization problem and includes the equilibrium equations as equality constraints. In this way, it is not necessary to solve the equilibrium equation per iteration; the equilibrium is only obtained at the end of the optimization process. In this paper, the shape optimization problem is dealt with using the BEM formulation to define a SAND optimization problem that is solved using an interior point algorithm. Numerical results for two-dimensional linear elasticity problems are presented to illustrate the efficacy of the proposed technique.