Intrinsic Geometry for Shape Optimal Design With Analysis Model Compatibility

1994 ◽  
Author(s):  
James M. Widmann ◽  
Sheri D. Sheppard
Keyword(s):  
Shape Optimization ◽  
Geometric Modeling ◽  
Explicit Knowledge ◽  
Optimization Problems ◽  
Structural Response ◽  
Analysis Model ◽  
Intrinsic Geometry ◽  
Structural Shape ◽  
Structural Shape Optimization ◽  
Design Variables

Abstract This paper presents a comparison of geometric modeling techniques and their applicability to structural shape optimization. A method of shape definition based on intrinsic geometric quantities is then outlined. Explicit knowledge of curvature and arc length allow for a quantitative assessment of the compatibility of analysis model with the design model when using finite elements to determine structural response quantities. The compatibility condition is formalized by controlling finite element idealization error and is incorporated into the shape optimization model as simple bounds on the curvature design variables. Several examples of shape optimization problems are solved using sequential quadratic programming which proves to be an effective tool for maintaining the geometric equality constraints that arise from intrinsically defined curves.

An Algorithm for Automated Design Variable Selection in Structural Shape Optimization With Intrinsically Defined Geometry

1995 ◽  
Author(s):  
James M. Widmann ◽  
Sheri D. Sheppard
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Analysis Model ◽  
Structural Shape ◽  
Structural Shape Optimization ◽  
Design Variables ◽  
Sufficient Set ◽  
Compatibility Constraint ◽  
Selection Of

Abstract A major difficulty encountered in the shape optimization of structural components is the selection of an adequate set of shape design variables. The quality of the solution and the value of the optimal objective function depend on the chosen set of design variables. This paper presents an algorithm for the automated selection of intrinsically defined design variables to solve two-dimensional structural shape optimization problems. The algorithm arrives at a sufficient set of design variables by solving a series of optimization problems. Using the results of intermediate solutions, the algorithm adaptively refines the set of design variables until the solution converges. The algorithm specifies the addition and deletion of design variables and makes use of a model compatibility constraint to determine whether the analysis model must be updated. Two examples are presented which illustrate the effectiveness of the algorithm.

Structural Shape Optimization Wth Error Control

1994 ◽  
Author(s):  
Pierre Duysinx ◽  
WeiHong Zhang ◽  
HaiGuang Zhong ◽  
Pierre Beckers ◽  
Claude Fleury
Keyword(s):  
Shape Optimization ◽  
Computer Aided Design ◽  
Adaptive Mesh Refinement ◽  
Error Control ◽  
Optimization Procedure ◽  
Adaptive Mesh ◽  
Structural Shape ◽  
Structural Shape Optimization ◽  
Design Variables ◽  
Recent Developments

Abstract A robust and automatic shape optimization procedure is presented in this paper, which incorporates recent developments in the field of computer-aided design (CAD) of mechanical structures, such as geometric modelling, automatic selection of independent design variables, sensitivity analysis using reliable mesh perturbation schemes, error estimation and adaptive mesh refinement. A numerical example is given to show the efficiency of the procedure.

Evolutionary Structural Shape Optimization Based on Adaptive FEM and Boundary Representation of B-Spline

2012 ◽  
Vol 562-564 ◽  
pp. 1575-1582
Author(s):  
Sheng Li Gu ◽  
Fu Ming Wang
Keyword(s):  
Shape Optimization ◽  
Boundary Representation ◽  
Structural Shape ◽  
B Spline ◽  
B Splines ◽  
Structural Shape Optimization ◽  
Evolutionary Structural Optimization ◽  
Design Variables ◽  
Adaptive Fem ◽  
Element Error

This paper presents a structural shape optimization algorithm based on the evolutionary structural optimization (ESO) method in conjunction with element error estimate and adaptive FEM. B-splines are used to describe the boundary of the design domain; the shape of these B-splines is governed by a set of master nodes which can be taken as the design variables. The optimal shape of the design boundary with constant stress is achieved iteratively by the movement and update of the position of the master nodes based on nodal stress leveling. The result quality, in terms of accuracy and efficiency, is tested and discussed with an analytical solution.

scholarly journals A variational formulation for computing shape derivatives of geometric constraints along rays

2020 ◽  
Vol 54 (1) ◽  
pp. 181-228 ◽  
Author(s):  
Florian Feppon ◽  
Grégoire Allaire ◽  
Charles Dapogny
Keyword(s):  
Velocity Field ◽  
Shape Optimization ◽  
Explicit Knowledge ◽  
Optimization Problems ◽  
Geometric Constraints ◽  
Normal Vector ◽  
Minimum Thickness ◽  
Full Generality ◽  
Structural Shape ◽  
Shape Derivatives

In the formulation of shape optimization problems, multiple geometric constraint functionals involve the signed distance function to the optimized shape Ω. The numerical evaluation of their shape derivatives requires to integrate some quantities along the normal rays to Ω, a challenging operation to implement, which is usually achieved thanks to the method of characteristics. The goal of the present paper is to propose an alternative, variational approach for this purpose. Our method amounts, in full generality, to compute integral quantities along the characteristic curves of a given velocity field without requiring the explicit knowledge of these curves on the spatial discretization; it rather relies on a variational problem which can be solved conveniently by the finite element method. The well-posedness of this problem is established thanks to a detailed analysis of weighted graph spaces of the advection operator β ⋅ ∇ associated to a C1 velocity field β. One novelty of our approach is the ability to handle velocity fields with possibly unbounded divergence: we do not assume div(β) ∈ L∞. Our working assumptions are fulfilled in the context of shape optimization of C2 domains Ω, where the velocity field β = ∇dΩ is an extension of the unit outward normal vector to the optimized shape. The efficiency of our variational method with respect to the direct integration of numerical quantities along rays is evaluated on several numerical examples. Classical albeit important implementation issues such as the calculation of a shape’s curvature and the detection of its skeleton are discussed. Finally, we demonstrate the convenience and potential of our method when it comes to enforcing maximum and minimum thickness constraints in structural shape optimization.

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