Shape Optimisation of Assembled Plate Structures with the Boundary Element Method (original) (raw)

A Simple Boundary Element Formulation for the Shape Optimization of Planar Structures

Proceedings of the Seventh International Conference on Computational Structures Technology, 2004

For the design of nuclear equipment like pressure vessels, steam generators, and pipelines, among others, it is very important to optimize the shape of the structural systems to withstand prescribed loads such as internal pressures and prescribed or limiting referential values such as stress or strain. In the literature, shape optimization of frame structural systems is commonly found but the same is not true for continuous structural systems. In this work, the Boundary Element Method (BEM) is applied to simple problems of shape optimization of 2D continuous structural systems. The proposed formulation is based on the BEM and on deterministic optimization methods of zero and first order such as Powell's, Conjugate Gradient, and BFGS methods. Optimal characterization for the geometric configuration of 2D structure is obtained with the minimization of an objective function. Such function is written in terms of referential values (such as loads, stresses, strains or deformations) prescribed at few points inside or at the boundary of the structure. The use of the BEM for shape optimization of continuous structures is attractive compared to other methods that discretize the whole continuous. Several numerical examples of the application of the proposed formulation to simple engineering problems are presented.

Analysis of Dual Boundary Element in Shape Optimization

IOSR Journal of Mechanical and Civil Engineering, 2016

The numerical analysis with dual boundary element method for shape optimal design in twodimensional linear elastic structures is proposed. The design objective is to minimize the structural compliance, subject to an area constraint. Sensitivities of objective and constraint functions, derived by means of Lagrangean approach and the material derivative concept with an adjoint variable technique, are computed through analytical expressions that arise from optimality conditions. The dual boundary element method, used for the discretization of the state problem, applies the stress equation for collocation on the design boundary and the displacement equation for collocation on other boundaries. The perturbation field is described with linear continuous elements, in which the position of each node is defined by a design variable. Continuity along the design boundary is assured by forcing the end points of each discontinuous boundary element to be coincident with a design node. The optimization problem is solved by the modified method of feasible directions available in the PYOPT program and the accuracy and efficiency of the analysis is assessed through two examples of a plate with a hole, making this formulation ideal for the study of shape optimal design of structures.

Structural shape optimization—A survey

Computer Methods in Applied Mechanics and Engineering, 1986

This paper is a survey of structural shape optimization with an emphasis on techniques dealing with shape optimization of the boundaries of two-and three-dimensional bodies. Attention is focused on the special problems of structural shape optimization which are due to a finite element model which must change during the optimization process. These problems include the requirement for sophisticated automated mesh generation techniques and careful choice of design variables. They also include special problems in obtaining sufficiently accurate sensitivity derivatives.

Multiparameter structural shape optimization by the finite element method

International Journal for Numerical Methods …, 1978

The problem of optimal design of the shape of a free or internal boundary of a body is formulated by assuming the boundary shape is described by a set of prescribed shape functions and a set of shape parameters. The Optimization procedure is reduced to determination of these parameters. For constant volume or material cost constraint, the optimality conditions are derived for the case of mean compliance design of elastic structures of a non-linear material. Some additional conditions for the global minimum of the mean compliance are proved. The most typical cases of boundary variations are discussed. The optimal shape problem is next formulated by means of the finite element method and the iterative solution algorithm is discussed by using the optimality criteria. Several simple numerical examples are included.

Optimization Of Curved Plated Structures With The Finite Strip And Finite Element Methods

Transactions of the VŠB – Technical University of Ostrava, Civil Engineering Series., 2015

The aim of this study is to compare two available numerical tools for solving of partial differential equations for the optimal design of structures. In the past years numerous methods were developed for topology optimization, from these we have adopted the optimality criteria (OC) approach. The main idea is that we state the optimal conditions, that the minimizer has to fulfil at the end of an iterative proves. This method however is not a general one, only advantageous in the case of separable problems, but comes with fast speed, easy programming, and a relative insensitivity of computational time to the number of variables. In the paper we suggest a new method for the elimination of a numerical error, the so called ‘checkerboard pattern’. In the presented examples we applied one loading case and an elastic material behaviour. The cost function is the net weight of the structure and upper bound of the compliance is set as the optimality constraint.

Boundary integral equation method for shape optimization of elastic structures

International Journal for Numerical Methods in Engineering, 1988

A general method for shape design sensitivity analysis as applied to plane elasticity problems is developed with a direct boundary integral equation formulation, using the material derivative concept and adjoint variable method. The problem formulation is very general and a complete consideration is given to describing the boundary variation by including the tangential component of the velocity field. The method is then applied to obtain the sensitivity formula for a general stress constraint imposed over a small part of the boundary. The accuracy of the design sensitivity analysis is studied with a fillet and an elastic ring design problem. Among the several numerical implementations tested, the second order boundary elements with a cubic spline representation of the moving boundary have shown the best accuracy. A smooth characteristic function is found to be better than a plateau function for localization of the stress constraint. Optimal shapes for the two problems are presented to show numerical applications.

Structural shape optimisation using boundary elements and the biological growth method

Structural and Multidisciplinary Optimization, 2004

A numerical evolutionary procedure for the structural optimisation for stress reduction of twodimensional structures is presented in this paper. The proposed procedure couples the biological growth method (BGM) with the boundary element method (BEM). The boundary-only intrinsic characteristic of BEM together with its accuracy in the boundary displacement and stress solutions make BEM especially attractive for solving shape-optimisation problems. Two formulations of BEM are used in this work: the standard for two-dimensional elastostatics for the stress analysis and the dual reciprocity method (DRM), which is used to model the swelling or shrinking of the material. Two examples are analysed to illustrate the proposed methodology and to demonstrate its versatility and robustness.