Shape And Stress Analysis Of Membrane Shell Antenna Structure Based On Meshless Method

Recently,membrane reflector is a new type reflector developed in recent years and has become an important part of antenna structure in the aerospace industry.It is of great significance to develop high efficient and high precision engineering numerical methods for membrane problems based on the membrane torque-free theory.Compared with the finite element numerical method,the Meshless method only needs node information and does not depend on the element to construct the approximate function,which has obvious advantages in solving the problems caused by cell distortion.Based on this,this thesis uses Elementfree Galerkin method(EFG)to study the bending problem of thin plate and the form-finding analysis of reflector structure of membrane antenna.This main work is as follows:1)Research and numerical analysis of the Element-free Galerkin method based on Moving Least Squares(MLS)approximation.Firstly,the MLS approximation function and its 1st-3rd derivative are given,and explore the influence rules of its basis function and weight function on the high-order continuity of the approximate function and its derivative.Then,for the elastic mechanics problem,the solving process of Element-free Galerkin method based on MLS approximation is described in detail.Finally,the EFG program is written based on MATLAB numerical software to analyze the cantilever beam.The feasibility of the EFG method and the correctness of the program are verified by comparing the analytical solution and the finite element software ANSYS simulation results.2)Analysis of Kirchhoff plate bending problem based on Element-free Galerkin method.Firstly,the differential governing equations and boundary conditions of thin plate bending are deduced based on theory of small deflection of thin plate.Then,the nodal deflection field functions are approximated using the higher-order continuity of the MLS,and establish the Element-free Galerkin discrete equation of Kirchhoff plate bending problem.Finally,the EFG method program is programmed to analyze the numerical examples of square and circular thin plates,and explore the influence rules of domain influence,basis function,weight function and node density on the calculation accuracy.By comparing the ANSYS simulation results,it is concluded that the EFG method is correct and efficient for solving the bending problem of thin plate.3)Shape and stress analysis of the membrane antenna reflector structure base on EFG method.Firstly,this chapter systematically expounds the orthogonal curvilinear coordinate system and the theory of membrane torque-free theory.Then,the field nodes are generated based on the curvilinear coordinates,and the displacement function of the membrane midsurface is approximated by MLS.Based on the energy variation principle,the Element-free Galerkin discrete equations for cylindrical and parabolic membrane reflector structures are derived.Finally,the EFG program of the membrane structure is written by MATLAB to calculate and analyze the cylindrical and parabolic membrane reflectors respectively.Meanwhile,compared with the ANSYS software to establish finite element model for solving the process,in order to highlight the efficiency of EFG method in calculating the membrane problem and the advantages of simplicity in model construction.4)A form-finding analysis strategy for the membrane reflector based on EFG method.Firstly,an optimization model for form-finding analysis of membrane reflector based on Meshless method is constructed.Then,an optimization algorithm is written by MATLAB to calculate the shape finding iteration of the membrane reflector,determine the optimal initial geometric configuration and calculate the better surface precision.