The Research And Realization Of Plane Element In Largeincrement Method

Large Increment Method (LIM) is put forward for material nonlinear problems inrecent years, which is a new finite element method based on force method. Thegeneralized inverse theory and optimization method are applied in the new algorithm.By using generalized inverse method, LIM deals with equilibrium equation directly andgets a set of hypothetical generalized internal force of the structure system. This innerforce is a particular solution of the equilibrium equations. Then take advantage ofoptimization algorithm to translate the structural analysis problem into an optimizationprocedure. The optimization procedure is in separate loading step and does not rely onother loading step. So, the length of loading step only depends on whether time samplepoints of loading procedure could reflect real loading history (loading or unloading).This is extremely different with incremental process whose length of loading step isassociated with accuracy and convergence. Large increment method is named by this.Compared with traditional displacement finite element method, LIM has theadvantage of higher accuracy of stress, shorter computational time and easier to parallelcompute. With the effort of predecessors, LIM already has a strict mathematical proofand theoretical basis. Its advantages of higher accuracy and shorter computational timeare verified in analysis of one dimension bar structure and frame structure. Howeverbefore the work of this thesis, the existing research about LIM is be restricted totheoretical study and parallel computation. It is only used in skeletal structure and can’tsolve large scale computing problems. It is far from widely used in engineering. So, it isan emergency to build element types of LIM to let the algorithm meets the requirementas soon as possible.The main content of this thesis is on the application and expansion of LIM in planesolid mechanics. Build two dimension entity element types to fill in the element library.Combined with the fact that LIM is based on force method, this research creativelyproposes a new element type which is different with nodal force element type in FEM.The new element type is named ‘stress element type’. The stress field and displacementfield of Stress element are interpolated respectively. Linearly independent coefficientsof stress interpolation function are defined element generalized inner forces as the basicunknown quantity of LIM. To avoid the mismatch between elemental stress field anddisplacement field and spurious zero energy modes, a selecting principle of elemental basic unknown quantity is proposed in terms of the number of rigid body displacementmodes and degrees of freedom. Based on the principle, stress element library is builtwhich contains twelve elements applying different geometrical shapes and differentstress functions. Numerical examples clearly show that computational accuracy of stresselements in LIM meet operating requirements. The author independently completed allthe writing and debugging of the program of stress elements in LIM. The relatedprogram segment see appendix in this thesis.The stress elements could be used in traditional displacement FEM. Though somemathematical treatments, elemental generalized stiffness matrix of stress element willbe obtained. It has similar effect with stiffness matrix which base on method ofweighted residuals. But it does not have physical significance. Elemental patch tests aredone to test the convergence of every stress element. The results of fundamentalsolution patch tests show that all of stress elements meet consistency requirement andstability condition. In higher-order patch tests, the performance of stress element isbetter than the element without reduced integration in FEM.