Numerical Analysis Applied to Nonlinear Problems
- PDF / 515,647 Bytes
- 7 Pages / 432 x 648 pts Page_size
- 109 Downloads / 233 Views
Numerical Analysis Applied to Nonlinear Problems E. Pineda León1, A. Rodríguez-Castellanos2, M.H. Aliabadi3 1 Escuela Superior de Ingeniería y Arquitectura, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos s/n, México D.F. 2 Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, Gustavo A Madero, México D.F. 3 Department of Aeronautical Engineering, Imperial College London, South Kensington campus, London SW72AZ ABSTRACT The present paper shows the applicability of the Dual Boundary Element Method to analyze plastic, visco-plastic and creep behavior in fracture mechanics problems. Several models with a crack, including a square plate, a holed plate and a notched plate are analyzed. Special attention is taken when the discretization of the domain is done. In Fact, for the plasticity and viscoplasticity cases only the region susceptible to yielding was discretized, whereas, the creep case required the discretization of the whole domain. The proposed formulation is presented as an alternative technique to study this kind of non-linear problems. Results from the present formulation are compared to those of the well-established Finite Element Technique, and they are in good agreement. Important fracture mechanic parameters such as KI, KII, J- and Cintegrals are also included. In general, the results, for the plastic, visco-plastic and creep cases, show that the highest stress concentrations are in the vicinity of the crack tip and they decrease as the distance from the crack tip is increased. INTRODUCTION For many years, problems of stress analysis in industry have been solved using Finite Difference Method and the Finite Element Method (FEM). FEM and the Boundary Element Method (BEM) have attained a level of development that has made them necessary tools for modern design engineers. The FEM is routinely used as a general analysis tool. The BEM applicability at present is not as wide ranging as FEM, however the method has become established as an effective alternative to FEM in several important areas of engineering which include acoustics and fracture mechanics. The attraction of BEM can be attributed to the reduction in dimensionality of the problem; for two-dimensional problems, only the lineboundary of the domain needs to be discretized into elements. This means that, compared to domain type analysis techniques, a boundary element analysis can result in substantial reduction in modelling effort. In BEM, for certain nonlinear problems such as plasticity and creep part or the whole of the domain also needs to be discretized. However, only the boundary displacements and tractions are treated as unknown and hence the system matrix remains of the same size as an equivalent elastic problem (see for example Ref. [1]). BEM has been applied to elastoplastic problems since the early 1970s with the work of Swedlow and Cruse [24] and Richardella [21], who implemented the von Mises criterion for 2D problems using piecewise constant interpolation for the plastic strains. Later on, at the beginning
Data Loading...
