Research On Quasi-conforming Plate/Shell Elements And Sheet-forming

As the core of CAE, finite element method is the most mature and widely used method in CAE. Quasi-conforming finite element method is an important and characteristic finite element method. The basic idea of quasi-conforming technique is that the strain-displacement equa-tions are weakened as well as the equilibrium equations, and the weighted weakened strains are approximated by element nodal displacement parameters. Starting from the basic idea, quasi-conforming technique construct a theoretical framework different from the traditional fi-nite element method, which have been used in many fields, especially in the plate/shell structure analysis. The element strain fields of the quasi-conforming method are approximated using polynomials and are integrated using string net functions. After satisfy the rank analysis, ex-tra terms in Taylor expansion of strains/displacements would not result in much improvement of the accuracy. The choice of interpolation functions is very important in quasi-conforming technique, including string net functions on the boundary and inner-field functions. This disser-tation does some researches on quasi-conforming plate/shell elements and some applications in sheet-forming, the main works include as follows:(1) Based on the Timoshenko’s beam function, we deduced a series of functions for the quasi-conforming Reissner-Mindlin plate element, and proposed a new4-node quadrilateral flat shell element. The exact displacement function of Timoshenko’s beam, from which the interpolated inner-field function is derived, is used as the string net function on the ele-ment boundary in the bending part. The re-constitution technique for the shear strains is adopted. The drilling degrees of freedom are added in the membrance part to improve membrane behavior. The flat shell element is of explicit form of the stiffness matrix, which is more effective when compared with elements using numerical integration. The element are free from membrane and shear locking, the interpolated inner-field function in the bending part is convenient for the post-processing.(2) A series of interpolation functions are deduced by using Timoshenko’s beam function, and a quasi-conforming triangular Reissner-Mindlin plate element is proposed. Two flat shell elements are constructed by adding different membrane part. The new shell elements preserve the advantages of the quasi-conforming technique, can be used for the analysis of both moderately thick and thin plate/shell structures, and the convergence for the very thin case can be ensured theoretically. (3) The quasi-conforming technique is applied in the sheet-forming. We deduced the formula-tions of quasi-conforming membrane element for the One-Step inverse forming technique by the assumption of plane stress and realized the algorithm by using the KM AS/OneStep platform. Numerical examples suggest that the method results in nearly the same accu-racy with the isoparametric membrane element using numerical integration, however more effective for the explicit stiffness matrix.(4) There are many holes in the meshes of car panel, some of them are intended cut-outs or unmodelled parts. However, some steps in the workflow of finite element analysis require a watertight model. A new hole-filling method of triangular meshes based on the above application is proposed. The proposed algorithm is powerful enough to recover the missing shape of finite element meshes, and can preserve the sharp feature. The refinement step of the algorithm guarantees the good quality of the patching meshes, which suit the need of applications in engineering.