Numerical and Experimental Investigation of an Elliptical Paraboloid Shell Model
For practical engineering purpose, a new flat shell element baptized (ACM_Q4SBE1) is presented in this paper. The formulated element can be used for the analysis of thin shell structures; no matter how the geometrical shape might be. Tests on standard problems have been examined. Since, the analysis of thin shell structures has generally been purely carried out on a theoretical basis; it is of importance to present some experimental results of an elliptical paraboloid under uniformly distributed load pressure. The results obtained from both numerical and experimental work are presented. Index Terms— Elliptical Paraboloid, finite element, flat shell element.
BASIS FOR DERIVATION OF MATRICES FOR THE DIRECT STIFFNESS METHOD
Previous developments in the direct stiffness method are reviewed. The advantages of extending the definitions to make the method a variational approach are cited. The finite element formulation of the method of minimum potential energy is given. Explicit requirements of potential energy displacements are presented, and a criterion insuring monotonic convergence is developed. Illustrative displacements yielding matrices resulting in monotonic convergence are included. Available matrices are reviewed with respect to the extended developments.
Large Deflections of Structures Subjected to Heating and External Loads
The method of direct formulation of the stiffness matr ix 1 3 is extended to include the effects of nonuniform heating and large deflections. The purpose is to develop an analytical tool for the treatment of actual structures. In the solution of aeroelastic problems the relations between forces and deflections must be determined. The usual stiffness matrix formulation of this relationship is limited to small temperature changes and small deflections. For large temperature changes additional terms are required. Also the problem becomes geometrically nonlinear when large deflections are involved. To overcome the inherent difficulties of the nonlinear problem for practical structures either an iterative or a step-bystep procedure must be used. The force-deformation relations necessary for this step-by-step or iterative approach are derived for an axially loaded member and for a plate element including the effects of thermal strains.