Construction And Application Analysis Of Compatible Plane Element

As one of the most commonly used numerical analysis tools in the field of engineering and scientific research,the status of the finite element method cannot be completely replaced by other methods for the time being.As the most widely used class of elements in finite element analysis,isoparametric element often leads to serious loss of computational accuracy due to mesh distortion.To address this problem,this topic uses linear transformation coordinates to establish the element displacement interpolation function,and introduces the energy compatibility condition of non-coordinated element in the process of solving the element shape function,forming a new shape-free finite element construction method.Based on this method,a linear 12-node compatible plane element XRQ12 and a geometrically nonlinear 8-node compatible plane element XRQ8 were developed in this thesis,and the compatible plane element was successfully embedded in the ADINA software.The main results are as follows:1.Based on the above-mentioned element construction method,the derivation formulas for the shape function of 8-node and 12-node compatible plane elements were established;and using the shape function of 12-node compatible plane element,the compatible plane element XRQ12 was developed for the linear small deformation problem.The element maintains the high-order completeness of the element displacement interpolation function for any grid shape.2.Based on the pre-processing module of ADINA software,the preprocessing program and the main calculation program of the compatible plane element XRQ12 were prepared by using For language;and the advantages of high computational accuracy and fast convergence of the element under the mesh distortion are proved by seven classical arithmetic examples,and the difficulty of volume locking of the traditional displacement element can be solved at the same time.3.Based on the large deformation finite element theory,the geometrically nonlinear finite element series of the compatible element XRQ8 was established by using the shape function of the 8-node compatible element.It was proved that the compatible element XRQ8 still has good stability、 grid insensitivity in geometrically nonlinear problems by six arithmetic examples.4.Based on the source program of ADINA8.1 version,the main calculation program and data conversion program of the compatible plane element were prepared,and the compatible element XRQ8 was successfully applied to the analysis of geotechnical problems.