Meshless Collocation Method For Electroelastic Analysis Of Piezoelectric Structure

Intelligent structures made of piezoelectric materials are widely designed and utilized nowadays in modern engineering applications such as micro-electro-mechanical systems(MEMS),biomedical,robot,military and many other scientific areas.The capability of energy transformation between the mechanical and electrical fields is frequently known as one of the most important features of piezoelectric materials.Due to the rather complicated nature of the coupled physical behaviors of piezoelectric materials,the most analytical or semianalytical models are not able to deal with the practical problems with complex geometries and loading conditions.As a consequence,efficient and robust numerical methods are required.Many numerical calculation methods have been proposed by domestic and foreign researchers.The meshless generalized finite difference method(GFDM)is considered as one of the novel domain-type strong-form meshless collocation methods.The local support region near the center node is formed in the computational domain according to the shortest distance criterion.In GFDM implementations based on multivariate Taylor series expansion and moving least squares techniques,the partial derivative of the physical quantity under consideration at a node can be expressed as a linear combination of the partial derivatives of neighboring nodes.This method not only avoids the meshing generation and numerical integration,but also provides the sparse resultant matrix,overcoming the problem of pathological generating matrices that exist in most meshless configuration methods.Thus,the method has the advantages of simple form,ease of use and implementation.This thesis is the first attempt to use the meshless generalized finite difference method to analyze the electro-mechanical coupling problem of piezoelectric structures,The main research work includes: 1.This thesis documents the first attempt to extend the meshless GFDM approach for the numerical solution of coupled electrical and mechanical equations governing the piezoelectricity problems.Rather than using a mesh,the GFDM uses a distribution of nodes to approximate the problem domain.In case of complex geometry and large deformations,this can save significant amounts of CPU-time and simplify the remeshing process.The present results agree very well with the exact solutions and the results calculated by using FEM(ABAQUS).2.An efficient GFDM-based method has been developed for electroelastic analysis of general 3D piezoelectric structures.In case of complex geometry and large deformations,this can save significant amounts of CPU-time and simplify the remeshing process.In general,the present scheme has high computational efficiency and good stability,and can be used as a competitive alternative for solving 3D piezoelectric problems.3.This study documents make the first attempt to apply the generalized finite difference method,a relatively new meshless collocation method,for the numerical solution of inverse electroelastic analysis of both 2D and 3D piezoelectric structures.In the inverse Cauchy problems,some part of the boundary data is missing and the numerical procedures may become very unstable,and small errors in the input data will greatly decrease the overall accuracy of the final results.For this reason,we tested the accuracy and stability of the present GFDM by adding different levels of noise into the input data.The results of numerical experiments by MATLAB show that the current GFDM is very effective for the simulation of the inverse Cauchy problems with coupled electroelastic structures,and the error can reach second-order accuracy even under the influence of adding large perturbations.As the perturbation increases,the error value becomes larger.By varying the number of nodes in the support domain,it is found that the generalized finite difference method is not sensitive to this parameter,and increasing the value of the number of selected points only increases the computational time.