Study On A Truss Structural Morphogenesis Technique In Restrictive Conditions Of Displacement

The design of structure should meet requirements of building function, especially structures supporting precision instruments and other special structures should meet the given requirements under loads, such as constraints of displacement , stress conditions and so on. Finite element equation meeting restrictive conditions is always nonlinear equation which includes implicit expression of design parameters in its stiffness matrix. It is difficult to determine structure shape,because the matrix is not always square matrix, even if the matrix is square matrix, it is not always nonsingular, general inverse matrix is an concept which is proposed to solve inverse problem of singular matrix and rectangle matrix, the concept is widely applied to areas of statistics, economics. In the 1990s, the professor Y. Hangai of Japan applies general inverse matrix to determine structural shape of cable membrane and he was successful to solve the problem of constructing the shape of the mobile system. In this paper, use the―generalized inverse matrix theory‖to study morphogenesis technique in restrictive conditions of displacement on the basis of a previous morphogenesis technique and theory.The basic ideas of morphogenesis technique are introduced which meets restrictive conditions of displacement. Its optimized mathematical model under displacement constraint is established. Solving method with generalized inverse matrix theory is raised and corresponding programs are coded by FORTRAN language. Initial models for truss structures are established; shape parameters or both shape parameters and cross-section area are taken as parameters respectively; then structural shape is optimized; the entire process of optimization is reviewed and the characteristics of the method is summarized. When set shape parameters as parameters and set both of shape parameters, cross-section area as parameter to optimize structural shape, the result is that shape is different, but meet restrictive conditions. In the entire process of optimizing, it is faster convergence when set both of shape parameters, cross-section area as parameter to optimize. Contrast the structural shape between the same loads and different loads.The affect of initial models and damping coefficient of step size to structure shapes is discussed,the initial model has great influence on final result , and the final shape is different after adjusting initial models. Damping coefficient also has influence on final result. Adjusting damping coefficient, many kinds of structure are obtained, when damping coefficient is larger, convergence is faster. However, if damping coefficient is too large, the structure which meets restrictive conditions of displacement can not be obtained.In this paper, the method is extended from plane truss to space truss, and its basic equations are established. Damping coefficient also has more influence on final results than space truss, but the initial model has less influence. Although their final shapes are different, they can meet restrictive conditions.In this paper, efficient optimization method is proposed. Examples confirm the solution is diverse, which meets restrictive conditions of displacement.