Assumed Displacement Quasi-Conforming Finite Element Method And Its Application In Exact-Geometry Based Analysis

Finite element method is the most important numerical analysis method, which plays great role in design, analysis and the life circle monitoring of industry products. The design method and concept of industry are deeply influenced by the finite element method. Quasi-conforming finite element method is an important and characteristic paradigm in finite element method. In quasi-conforming finite element method, the strain-displacement relationships are weakened along with the equilibrium equations; as a result the method is flexible and practicable, which can unify the conforming and non-conforming frame. The elements formulated with quasi-conforming are widely used in multiple industry areas, especially in the analysis of structure. Therefore, the research in quasi-conforming finite element method is import for its great science as well as the industry application value.This thesis is on the research of quasi-conforming finite element method. The work is composed of two parts. First, the assumed displacement quasi-conforming finite element framework is proposed based on the research of elastic plane and plate/shell problems. The element construction and performance analysis of quasi-conforming finite element method is improved. In the second part, the exact-geometry based analysis is introduced to quasi-conforming framework. A new method, the exact geometry based quasi-conforming analysis is proposed. With this method, the mesh is not needed for the analysis process. The method provides an important algorithm for the next generation analysis system which can unify the geometry design and analysis.In the first part of this thesis, the element construction method and algorithm theory are researched. The assumed displacement method is proposed to improve the selection rule for displacement and strain trial functions. With this method, the connection between displacement and strain fields are strengthened, which qualify the elements with better robustness and convergence performance. The calculation for shape function of displacement field is implemented in the quasi-conforming method, which is important for calculation for consistent mass matrix and load vector. The general derivative of the strain-displacement relation is proposed. For the convergence problem, the Taylor expansion test is introduced which can check the convergence rate of element formulation. This part of work is summarized as the "assumed displacement quasi-conforming finite element method" With assumed displacement quasi-conforming finite element method, a series of structural analysis elements are formulated which are applicable for industrial analysis. A four-node element for plane problem is directly formulated in rectangular coordinate system, and the isoparametric transformation and numerical analysis which is essential for traditional finite element method is avoidable. The element is simple and efficient with explicit stiffness matrix. The formulation is used in the inverse analysis of panel stamping and the performance is better than4-node isoparametric element with great efficiency. The plant and shell elements are formulated with assumed displacement quasi-conforming method. The elements have great performance in convergence rate and extensive tests are carried out for the complex structural analysis. The results by present plate and shell elements are compared with results from commercial analysis software package and the analytical solution, which shows that present elements are precise and applicable.Exact geometry based analysis is a new method which apply the geometry model directly for analysis and the process for generating finite element mesh from geometry model is avoided. The advantagement of exact geometry based analysis compared with traditional finite element method is that the computer aided design and analysis can be unified and the industry design and analysis processes are greatly improved. For problems which are sensitive of the geometry appearance, such as the buckling analysis of shell and the fluid analysis around the aircraft, exact geometry based analysis is especially suitable and can improve the precision.In the second part of this thesis, the exact geometry concept is applied in quasi-conforming finite element method and the exact geometry based quasi-conforming analyisis is proposed. In this method the isoparametric framework is broken and the polynomial basis functions are used to simulate the physical fields and non-uniform rational B spline for precise geometry model. The strain-displacement equations are softened and the complete set of basis functions are used to simulate the physical fields. With exact geometry based quasi-conforming method the precision of analysis is improved, which provides an alterate technique choise for exact geometry based analysis.With the geometry modeling core "ACIS", an exact geometry based analysis software framework is constructed, which is able to input, modify and output the standard geometry models. With exact geometry based quasi-conforming analysis, the one dimensional column element, beam element, two dimensional plane element and plate element are developed.This thesis is the inheritance and development for quasi-conforming finite element method. The formulation framework and theory of quasi-conforming are improved, and a set of efficient elements are formulated. The exact geometry concept is implemented in quasi-conforming method and a new method is proposed. The work of this thesis provides both theory basis and also technique storage for numerical analysis.