Improved shell finite elements for linear and nonlinear analysis of shell structures

Abstract

In this dissertation, the development of an improved degenerated shell element is presented for linear and nonlinear analysis of shell structures. The generality and simplictiy of the degenerated shell element have made it more and more employed in a wide range of sturctural problems. This element, however, has some significant drawbacks, e.g. shear/membrane locking phonemena and slow conver gence. To alleviate this deficiency, several techniques have been proposed. Among those, the notable ones are the selective or reduced integration, the addition of nonconforming mode and the substitute shear strain fields. The merits and demerits of these methods are discussed in this study. In the formulation of the new shell element, the combined use of three different techniques was made. They are; the enhanced interpolation of transverse shear strains in the natrual coordinate system to overcome the shear locking problem, the rduced integration technique in in-plane strains to avoid the membrane locking behavior and the selective addition of the nonconforming displacement modes to improve the element performances. The improvement obtainable by the new element may be attributed to the fact the merits of the above techniques are merged into the new shell elements in a complementary way. Subsequently the new formulations will be extended to finite element modeling of geometrically or materially nonlinear analysis of shell structrues and laminated composite shells. An incremental total Lagrangian formulation which allows the calculation of arbitrarily large displacements and rotations is prewented. In the formulation for plastic deformation, the concept of a layered element model is used and the Von Mises yield criterion is used to define the limit of plasticity. The resulting nonlinear equilibrium equations are solved by the Newton-Raphson method combined with load or displacement increment. An improved degenerated shell element has been developed based on the proposed con...