Theoretical Optimization Of Element-Free Galerkin Method And Its Application In Stability Of Composite Laminates

As a new numerical calculation tool,the element-free method is free from the dependence on the grid.It uses discrete nodes to construct the shape function.It does not need to be divided for the computational domain.The pre-processing process is simplified to a certain extent,and in the analysis process.The node layout in the whole domain can be adjusted to improve the calculation accuracy.The meshless Galerkin method is widely used in the element-free method.Its advantage lies in constructing orthogonal MLS interpolation,avoiding the ill-conditioned calculation matrix at the node,and repeating the calculation in the pre-processing.The calculation results have good results.Convergence and precision.At the same time,the method has good adjustability in the process of solution analysis.The calculation program can be adjusted according to the specific problem from the construction of approximation function,weight function selection and related parameter setting.The gridless Galerkin method has a short development time and still has shortcomings.The amount of calculation in the pre-processing is large,and the strong openness is easy to be affected by uncertain factors;the parameter selection lacks authoritative argumentation and guidance.In this paper,the non-grid Galerkin method calculation program and its application on the composite layer board are studied.The stability analysis problem of the composite layer board is discussed in depth by using the analysis and calculation program.Firstly,the paper introduces the advantages and applications of the element-free method compared with the traditional numerical method in engineering calculation.The purpose and main research contents of this paper are presented in the application of the meshless Galerkin method to the stability of composite laminates.Secondly,based on the variable scheme in the theory of meshless Galerkin method,the approximate scheme,the discrete scheme,the weight function type,and the essential boundary condition method are compared to determine the theoretical method of the element-free method used in this paper.The penalty function method is used to derive the governing equations.Thirdly,the error existing in the realization of the element-free method based on background mesh integral is analyzed and optimized.The properties of different weight functions are analyzed and compared,and the weight function is also studied.The selection of parameters and the influence of parameter values on the properties of the resulting shape function are compared and analyzed.The node layout methods such as node uniform distribution and adaptive adjustment method are compared and analyzed.The node is automatically generated by the editing program to ensure high efficiency.At the same time,the error test formula is derived,and the self-test program is added in the traditional algorithm to filter the background grid that does not meet the requirements and eliminate the nodes with low contribution.Finally,the optimization program is used to analyze the stability problem of the composite laminate,and the The governing equations of the combination of the grid Galerkin method and the composite layer theory,in the example,discuss the optimization of the weight function parameter range,the adaptive node distribution,the optimization of the integral method and the traditional scheme on the accuracy of the calculation results,and the literature The analytical solution and the finite element solution are related.At the end of the article,the research content of this paper is summarized,and the problems existing in the research process are put forward for the application research of element-free engineering.