A Method For The Analytical Description Of Topological Optimal Truss-like Structures

The post-processing problems of the topological optimization method based on truss-like structure model is studied.There are many methods for the discretization of truss-like structures,but most of them are not accurate or the discretization process is not reasonable.In order to solve this problem.Firstly,an analytical description method of truss-like structures is proposed.Then the truss-like structures by analytic expression can be described,and the distribution of members of the truss-like structures by analytic function can be precisely located.The establishment of function model,curve fitting and Matlab programming and other mathematical and computer means are involved in this process.Finally,four structural optimization problems are taken as examples to demonstrate the analytical description optimization results of truss-like structures.In addition,based on the analytical description method of truss-like structures,this paper discretizes the truss-like structures into discrete truss-like structures and uniform plates of uniform thickness with holes.Three kinds of discrete trusses and their corresponding perforated plates for the classical Michell truss problem are obtained.The research results of this paper mainly include the followings:(1)General polynomial function fitting method is proposed.The general polynomial function is established by spline interpolation method.The least square method is used to fit the linear description results of truss-like structures.The method is simple to operate,has a general optimization effect and can control the number of bars.However,the fitting range of this method is small and the error is relatively large.(2)A parameter function fitting method is proposed.The parametric function model was established with the arc length as the parameter,and the linear description results of truss-like structures were fitted by the least square method.The method has a large fitting range and good optimization effect.It is easier to calculate the bar length between two points on the rod by taking the arc length as the parameter.However,the method can not control the number of bars.(3)A high-dimensional parameter function fitting method is proposed.Based on the results of the parametric function fitting method,the coefficients of each member are taken as a group of data,and the higher dimensional parametric function is used for further fitting.The method has the best fitting effect,and the results show that the number of rods is adjustable and distributed evenly.But this method can only deal with cantilever beam problem at present.(4)A method of discretization of truss-like structures into discrete trusses and plates with holes is proposed.Based on the results of the analytical description method of truss-like structures,the method USES a series of mathematical and computer methods to discretize the truss-like structures into discrete trusses and uniform plates of uniform thickness.The position of the members of the discrete truss is accurate,the error is small and the number of members is adjustable.By using this method,the hole position of plate with hole is precise,the hole boundary is clear and the number of holes is adjustable.