Boundary Elements in Shape Optimal Design of Structures

1986 ◽  
pp. 199-231 ◽  
Author(s):  
C. A. Mota Soares ◽  
K. K. Choi
Keyword(s):  
Optimal Design ◽  
Boundary Elements

A Hybrid Shape Optimization Method Based on Implicit Differentiation and Node Removal Techniques

1993 ◽  
Author(s):  
P. Y. Shim ◽  
S. Mannoochehri
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Optimal Design ◽  
Design Methodology ◽  
Structural Integrity ◽  
Boundary Elements ◽  
Programming Algorithm ◽  
Element Analysis ◽  
Node Removal ◽  
Removal Technique

Abstract This paper presents a hybrid shape optimal design methodology using an implicit differentiation approach for sensitivity analysis and a node removal technique for shape alteration. The approach presented attempts to overcome the weaknesses inherent in each individual technique. The basic idea is to combine the sensitivity analysis, which forms the analytical basis for the algorithm, and a node removal technique, which grossly modifies the shape without the need for a remeshing after each iteration. The sensitivity analysis is based on the finite element equilibrium equation and the implicit differentiation technique. It examines the effect positional changes of the boundary nodes have on the stress values. Using the sensitivity results, a sequential linear programming algorithm is utilized to determine optimum positions of the boundary nodes. These optimization results are provided as inputs to an algorithm that decides which boundary nodes should be removed. By removing boundary nodes, the boundary elements change to either a triangular or a non-existent type. This shape modification procedure starts from the boundary elements and moves toward the internal elements. Only two iterations of finite element analysis are required to modify one boundary layer. To maintain the structural integrity and the connectivity of the elements in the model, a connectivity check is performed after each iteration. Three design examples are given to illustrate the accuracy and the steps involved in the proposed optimal design methodology.

Optimization of the Geometry of Shafts Using Boundary Elements

1984 ◽  
Vol 106 (2) ◽  
pp. 199-202 ◽  
Author(s):  
C. A. Mota Soares ◽  
H. C. Rodrigues ◽  
L. M. Oliveira Faria ◽  
E. J. Haug
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Nonlinear Programming ◽  
Boundary Element Method ◽  
Optimal Design ◽  
Boundary Elements ◽  
Linearization Method ◽  
Nonlinear Programming Problem ◽  
The Finite Element Method ◽  
Element Method

The problem of the optimization of the geometry of shafts is formulated in terms of boundary elements. The corresponding nonlinear programming problem is solved by Pshenichny’s Linearization method. The advantages of the boundary element method over the finite element method for optimal design of shafts are discussed, with reference to the applications.

Shape Optimal Structural Design Using Boundary Elements and Minimum Compliance Techniques

1984 ◽  
Vol 106 (4) ◽  
pp. 518-523 ◽  
Author(s):  
C. A. Mota Soares ◽  
H. C. Rodrigues ◽  
K. K. Choi
Keyword(s):  
Optimal Design ◽  
Structural Design ◽  
Degrees Of Freedom ◽  
Boundary Elements ◽  
Linearization Method ◽  
Two Dimensional ◽  
Structural Components ◽  
Advantages And Disadvantages ◽  
Minimum Compliance ◽  
Element Technique

Shape optimal design of two-dimensional elastic components is formulated using boundary elements. The design objective is to minimize compliance of the structure, subject to an area constraint. All degrees of freedom of the model are at the boundary and there is no need for calculating displacements and stresses in the domain. Formulations based on linear and quadratic boundary elements are developed. The corresponding nonlinear programing problem is solved by Pshenichny’s linearization method. The model is applied to shape optimal design of several elastic structural components. The advantages and disadvantages of the boundary element method over the finite element technique for shape optimal design of structures are discussed, with reference to applications.

Finite elements-boundary elements coupling for the movement modeling in two-dimensional structures

1992 ◽  
Vol 2 (11) ◽  
pp. 2035-2044 ◽  
Author(s):  
A. Nicolet ◽  
F. Delincé ◽  
A. Genon ◽  
W. Legros
Keyword(s):  
Finite Elements ◽  
Boundary Elements ◽  
Two Dimensional
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