Vassili V. Toropov

Multiparameter structural optimization using FEM and multipoint explicit approximations

A unified approach to various problems of structural optimization, based on approximation concepts, is presented. The approach is concerned with the development of the iterative technique, which uses in each iteration the information gained at several previous design points (multipoint approximations) in order to better fit constraints and/or objective functions and to reduce the total number of FE analyses needed to solve the optimization problem. In each iteration, the subregion of the initial region in the space of design variables, defined by move limits, is chosen. In this subregion, several points (designs) are selected, for which response analyses and design sensitivity analyses are carried out using FEM. The explicit expressions are formulated using the weighted least-squares method. The explicit expressions obtained then replace initial problem functions. They are used as functions of a particular mathematical programming problem. Several particular forms of the explicit expressions are considered. The basic features of the presented approximations are shown by means of classical test examples, and the method is compared with other optimization techniques.

Simulation approach to structural optimization

A unified approach to various problems of structural optimization is presented. It is based on a combination of mathematical models of different complexity. The models describe the behaviour of a designed structure. From the computational point of view, it is connected with the sequential approximation of design problem constraints and/or an objective function. In each step, a subregion of the initial search region in the space of design variables is chosen. In this subregion, various points (designs) are selected, for which response analyses are carried out using a numerical method (mostly FEM). Using the least-squares method, analytical expressions are formulated, which then replace the initial problem functions. They are used as functions of a particular mathematical programming problem. The size and location of sequential subregions may be changed according to the result of the search. The choice of one particular form of the analytical expressions is described. The application of the approach is shown by means of test examples and comparison with other optimization techniques is presented.

Identification of material parameters in constitutive model for sheet metals from cyclic bending tests

Abstract This paper deals with the identification of material parameters in a constitutive model for sheet metals using the bending moment versus curvature diagrams obtained by cyclic bending tests. The model can describe the cyclic strain hardening by the isotropic hardening and the Bauschinger effect by the kinematic hardening. An optimization technique based on the iterative multipoint approximation concept was used for the identification of the material parameters. This paper describes the experimentation, the fundamentals and the technique of the identification problem, and the verification of this approach.

Formulation of the Optimal Latin Hypercube Design of Experiments Using a Permutation Genetic Algorithm

The choice of location of the evaluation points is important in response surface generation, especially when the evaluations are expensive. Space-filling designs can be used to specify the points so that as much of the design space is sampled as possible with the minimum number of response evaluations. One popular technique is the optimal Latin hypercube design of experiments. However, its generation is non-trivial, time consuming and is – but for the simplest problems – infeasible to carry out by enumeration. Therefore, solving this problem requires an optimization technique to search the design space. As the problem is discrete, it is ideally suited to the use of discrete optimization techniques such as genetic algorithms. This paper describes a method for generating optimal latin hypercubes using a permutation genetic algorithm and compares it with a standard binary genetic algorithm. The objective of the optimization is based on minimizing a function that is analogous the potential energy of the system of material points. The developed method offers considerable improvements over previous solutions; it generates better solutions and the computational effort in reaching those solutions is significantly reduced.

Empirical modelling of shear strength of RC deep beams by genetic programming

Abstract This paper investigates the feasibility of using genetic programming (GP) to create an empirical model for the complicated non-linear relationship between various input parameters associated with reinforced concrete (RC) deep beams and their ultimate shear strength. GP is a relatively new form of artificial intelligence, and is based on the ideas of Darwinian theory of evolution and genetics. The size and structural complexity of the empirical model are not specified in advance, but these characteristics evolve as part of the prediction. The engineering knowledge on RC deep beams is also included in the search process through the use of appropriate mathematical functions. The model produced by GP is constructed directly from a set of experimental results available in the literature. The validity of the obtained model is examined by comparing its response with the shear strength of the training and other additional datasets. The developed model is then used to study the relationships between the shear strength and different influencing parameters. The predictions obtained from GP agree well with experimental observations.

Inverse approach to identification of material parameters of cyclic elasto-plasticity for component layers of a bimetallic sheet

Abstract The present paper proposes a novel approach to the identification of the mechanical properties of individual component layers of a bimetallic sheet. In this approach, a set of material parameters in a constitutive model of cyclic elasto-plasticity are identified for the two layers of the sheet simultaneously by minimizing the difference between the experimental results and the corresponding results of numerical simulation. This method has an advantage of using the experimental data (tensile load vs strain curve in the uniaxial tension test and the bending moment vs curvature diagram in the cyclic bending test) for a whole bimetallic sheet but not for individual component layers. An optimization technique based on the iterative multipoint approximation concept is used for the identification of the material parameters. This paper describes the experimentation, the fundamentals and the technique of the identification, and the verification of this approach using two types of constitutive models (the Chaboche-Rousselier and the Prager models) for an aluminum clad stainless steel sheet.

Identification of parameters for air permeability of shotcrete tunnel lining using a genetic algorithm

Abstract This paper describes an identification process for determination of material parameters in a constitutive relationship, describing time dependency of air permeability of shotcrete tunnel lining. A numerical model has been developed to predict the air losses from tunnel face and perimeter walls in compressed air tunnelling. Field data from a Tunnel in Germany has been used to verify and calibrate the numerical model. A relationship has been established to describe the variation of the air permeability of shotcrete tunnel lining with time and the technique of parameter identification has been used to determine the parameters of this relationship. A genetic algorithm has been used in the optimisation procedure. It has been shown that time dependency of permeability of shotcrete plays a key role in controlling the air losses in driving tunnels under compressed air with shotcrete as a temporary or permanent lining and this time dependency should be taken into account in design.

Design optimization of structural steelwork using a genetic algorithm, FEM and a system of design rules

In this paper a structural optimization technique based on a modified genetic algorithm (GA) is presented. The technique is developed to deal with discrete design optimization of structural steelwork. Also, the paper discusses the effect of different approaches, employed for the determination of the effective buckling length of a column, on the optimum design. In order to consider realistic steelwork design problems, a modified GA has been linked to a system of structural design rules (British Standards BS 5950 and BS 6399), interacting with a finite element package. In the formulation of the optimization problem, the objective function is the total weight of the structural members, as it gives a reasonably accurate estimation of the cost. The cross‐sectional properties of the structural members, which form the set of design variables, are chosen from two separate catalogues (universal beams and columns) covered by the British Standard BS 4. The minimum weight designs of two plane steel frame structures subjected to realistic multiple loading cases are obtained. These examples show that the modified GA in combination with structural design rules and more accurate analysis provides an efficient tool for practicing designers of steel frame structures. Finally, it is shown that the resulting design optimization is considerably influenced by a specific choice of a technique employed for the evaluation of the effective buckling length of structural members.

NEW DEVELOPMENTS IN STRUCTURAL OPTIMIZATION USING ADAPTIVE MESH REFINEMENT AND MULTIPOINT APPROXIMATIONS

Combining Shape Optimization (SO) with Adaptive Mesh Refinement (AMR) potentially offers a higher accuracy and higher computational efficiency, especially if the applied target error for AMR is reduced in the course of the optimization process. The disadvantage of that approach is that the rate of convergence of the corresponding optimization processes can be significantly lower as compared to processes which apply a fixed target error for AMR. In the present paper the so-called Multipoint Approximation Method (MAM) is used as a basis for SO in conjunction with AMR. Several techniques for improvement of the rates of convergence are presented and investigated. Firstly, alternative algorithms for determining the approximation functions using a weighted least squares method are investigated. The focus is on weights which depend on the discretization errors. Secondly, different strategies for moving and resizing the search sub-regions in the space of design variables are presented. The proposed methods are il...

Optimization of geometrically nonlinear thin-walled structures using the multipoint approximation method

The present study concentrates on the optimization of geometrically nonlinear shell structures using the multipoint approximation approach. The latter is an iterative technique, which uses a succession of approximations for the implicit objective and constraint functions. These approximations are formulated by means of multiple regression analysis. In each iteration the technique enables the use of results gained at several previous design points. The approximate functions obtained are considered to be valid within a current subregion of the space of design variables defined by move limits. A geometrically nonlinear curved triangular thin shell element with the corner node displacements and the mid-side rotations as degrees of freedom is used for the FE analysis. The influence of initial shape imperfections on the optimum designs is investigated. Imperfections are considered as a shape distortion proportional to the lowest buckling modes of the perfect structure. Displacement, stress, and stability constraints are taken into account. To prevent finite element solutions from becoming unstable during the optimization process, a simple strategy for avoiding passage of stability points is applied. Some numerical examples are solved to show the practical use and efficiency of the technique presented.