Sun Huan-chun

Analytical Treatment of Boundary Integrals in Direct Boundary Element Analysis of Plan Potential and Elasticity Problems

An analytical scheme, which avoids using the standard Gaussian approximate quadrature to treat the boundary integrals in direct boundary element method (DBEM) of two-dimensional potential and elastic problems, is established. With some numerical results, it is shown that the better precision and high computational efficiency, especially in the band of the domain near boundary, can be derived by the present scheme.

Topology optimization design of continuum structures under stress and displacement constraints

Topology optimization design of continuum structures that can take account of stress and displacement constraints simultaneously is difficult to solve at present. The main obstacle lies in that, the explicit function expressions between topological variables and stress or displacement constraints can not be obtained using homogenization method or variable density method. Furthermore, large quantities of design variables in the problem make it hard to deal with by the formal mathematical programming approach. In this paper, a smooth model of topology optimization for continuum structures is established which has weight objective considering stress and displacement constraints based on the independent-continuous topological variable concept and mapping transformation method proposed by Sui Yunkang and Yang Deqing. Moreover, the approximate, explicit expressions are given between topological variables and stress or displacement constraints. The problem is well solved by using dual programming approach, and the proposed element deletion criterion implements the inversion of topology variables from the discrete to the continuous. Numerical examples verify the validity of proposed method.

Virtual boundary element-linear complementary equations for solving the elastic obstacle problems of thin plate

Abstract A thin plate with arbitrary shape and arbitrary boundary conditions has gap δ( X ) between the bottom surface of plate and the elastic winkler foundation. When the thin plate is subjected to the action of transverse loads, the deflextion W ( X ) at point x will be obstructed by the elastic foundation, if the deflection W ( X ) > δ ( X ). So the problem of finding W ( X ) is a nonlinear one. In this paper the theory of the virtual energy inequality equation and the virtual boundary element method (VBEM) are used to formulate a system of linear complementary equations under the condition that all boundary conditions are satisfied. Two examples are solved numerically by Lemke algorithm. The results of one example coincide very well with that of the analytical solution while δ ( X ) = 0, and the results of the second example agree very well with the symmetrical conditions, because there is no analytical solution in this example. The advantages of this method are that there are no singular integrals to be handled and the iterative calculation is totally avoided.

Unified Way for Dealing With Three-Dimensional Problems of Solid Elasticity

Unified way for dealing with the problems of three dimensional solid, each type of plates and shells etc. was presented with the virtual boundary element least squares method(VBEM). It proceeded from the differential equations of three-dimensional theory of elasticity and employs the Kelvin solution and the least squares method. It is advantageous to the establishment of the models of a software for general application to calculate each type of three-dimensional problems of elasticity. Owing to directly employing the Kelvin solution and not citing any hypothesis, the numerical results of the method should be better than any others. The merits of the method are highlighted in comparison with the direct formulation of boundary element method (BEM). It is shown that coefficient matrix is symmetric and the treatment of singular integration is rendered unnecessary in the presented method. The examples prove the efficiency and calculating precision of the method.

A Method for Topological Optimization of Structures with Discrete Variables under Dynamic Stress and Displacement Constraints

A method for topological optimization of structures with discrete variables subjected to dynamic stress and displacement constraints is presented. By using the quasistatic method, the structure optimization problem under dynamic stress and displacement constraints is converted into one subjected to static stress and displacement constraints. The comprehensive algorithm for topological optimization of structures with discrete variables is used to find the optimum solution.

Formulation of boundary element-linear complementary equation for the frictional elastic contact problems

Boundary element-linear complementary equations are formulated to solve elastic contact problems with Coulomb frictions. It is also a new attempt to solve free boundary problems in solid mechanics by means of boundary element-mathematical programming techniques.

Equivalent Boundary Integral Equations with indirect unknowns for thin elastic plate bending theory

Equivalent Boundary Integral Equations (EBIE) with indirect unknowns for thin elastic plate bending theory, which is equivalent to the original boundary value problem, is established rigorously by mathematical technique of non-analytic continuation and is fully proved by means of the variational principle. The previous three kinds of boundary integral equations with indirect unknowns are discussed thoroughly and it is shown that all previous results are not EBIE.

A combinatorial algorithm for the discrete optimization of structures

The definition of local optimum solution of the discrete optimization is first given, and then a comprehensive combinatorial algorithm is proposed in this paper. Two-level optimum method is used in the algorithm. In the first level optimization, an approximate local optimum solution is found by using the heuristic algorithm, relative difference quotient algorithm, with high computational efficiency and high performance demonstrated by the performance test of random samples. In the second level, a mathematical model of (-1, 0, 1) programming is established first, and then it is changed into (0, 1) programming model. The local optimum solution X* will be from the (0, 1) programming by using the delimitative and combinatorial algorithm or the relative difference quotient algorithm. By this algorithm, the local optimum solution can be obtained certainly, and a method is provided to judge whether or not the approximate optimum solution obtained by heuristic algorithm is an optimum solution. The above comprehensive combinatorial algorithm has higher computational efficiency.

Approach for Layout Optimization of Truss Structures With Discrete Variables Under Dynamic Stress,Displacement and Stability Constraints

A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures include two levels, i.e., the topology optimization and the shape optimization. In each level, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.

Equivalent boundary integral equations with indirect variables for plane elasticity problems

The exact form of the exterior problem for plane elasticity problems was produced and fully proved by the variational principle. Based on this, the equivalent boundary integral equations (EBIE) with direct variables, which are equivalent to the original boundary value problem, were deduced rigorously. The conventionally prevailing boundary integral equation with direct variables was discussed thoroughly by some examples and it is shown that the previous results are not EBIE.