GEOMETRIC AND MATERIAL NONLINEAR DYNAMIC ANALYSIS OF COMPLEX SHELLS (FINITE ELEMENTS, ELASTIC-VISCOPLASTICITY, TIRE INFLATION, CONTACT)
Abstract
A 48 degree-of-freedom doubly curved quadrilateral thin shell element, including the effect of both material and geometric nonlinearities, is formulated and appropriate numerical procedures are adopted for the development of a systematic and efficient approach for static and dynamic nonlinear analysis of general shell structures. The Cartesian displacement functions are described by bicubic Hermitian polynomials in curvilinear coordinates. The geometry of the shell surface is modeled using variable-order polynomials. This may allow the stiffness formulation of the shell element to be linked to the geometric data bases created by the CAD systems. The geometric formulations employ the Lagrangian mode for description of motion. Only small strains and small rotations are allowed. The material formulations for nonlinear elastic-plastic and elastic-viscoplastic behavior, and for elastic laminated anisotropic constructions are considered. The spread of plastic zone in the shell is general and is allowed by using a layered model in the thickness direction, and by monitoring stress levels at points along the shell surface lying on Gauss integration grid. The incremental equations of motion are linearized about a given equilibrium state. The next state is obtained by providing a load- or displacement-increment for static analysis, and through numerical integration based on Newmark's generalized operator for dynamic analysis. Newton-Raphson iterations are performed in each solution step to insure equilibrium at the end of the step. A systematic choice of examples is solved and compared with available solutions to evaluate the formulations and procedures recommended. As an application of the present element, a detailed study of the static contact of an inflated radial automotive tire with rigid surface is conducted. An inflation analysis of tire is first carried out and then the results for footprint areas at different stages of contact; and resulting redistribution of stress and moment resultants, all of practical significance to the tire industry are obtained.
Degree
Ph.D.
Subject Area
Aerospace materials
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