摘要：In the last few years a number of numerical methods, later designated by the collective name of “generalized …nite element methods”, have been developed. Among those methods one can refer to the GFEM, Free Galerkin Method, hp-Clouds Method and Partition of Unity (PUFEM) method. Applications of the last two of then have been successfully developed for linear analysis based on Timoshenko beams, 2-D elasticity, plate and shells structural elements, through both, domain and boundary formulations. This paper describes a …rst application of the Partition of Unity method to small strain elasto-plasticity analysis. Following the method, a partition of unity is de…ned over the domain with reference to brick solid elements. Next, the hp-Cloud method is used to perform p-enrichment. The p-enrichment consists of globally de…ned polynomial. This global characteristic, as opposed to the standard form, based on local, intrinsic coordinates, is a source of the low mesh distortion sensitivity exhibited by the method. Also, it allows enrichment in particular regions and directions of the model (as corners and boundary layers), in a very predictable way. Classical elasto-plasticity model is used, with linear mixed hardening, J2 plastic surface and radial return method for stress integration. Preliminary numerical results are shown, which indicate good behavior of the formulation with respect to mesh distortion. Also, a clear demonstration is made, of the singularity which arises in the sti¤ness matrix of an undistorted element generated by this class of methods.
其他摘要：In the last few years a number of numerical methods, later designated by the collective name of “generalized …nite element methods”, have been developed. Among those methods one can refer to the GFEM, Free Galerkin Method, hp-Clouds Method and Partition of Unity (PUFEM) method. Applications of the last two of then have been successfully developed for linear analysis based on Timoshenko beams, 2-D elasticity, plate and shells structural elements, through both, domain and boundary formulations. This paper describes a …rst application of the Partition of Unity method to small strain elasto-plasticity analysis. Following the method, a partition of unity is de…ned over the domain with reference to brick solid elements. Next, the hp-Cloud method is used to perform p-enrichment. The p-enrichment consists of globally de…ned polynomial. This global characteristic, as opposed to the standard form, based on local, intrinsic coordinates, is a source of the low mesh distortion sensitivity exhibited by the method. Also, it allows enrichment in particular regions and directions of the model (as corners and boundary layers), in a very predictable way. Classical elasto-plasticity model is used, with linear mixed hardening, J2 plastic surface and radial return method for stress integration. Preliminary numerical results are shown, which indicate good behavior of the formulation with respect to mesh distortion. Also, a clear demonstration is made, of the singularity which arises in the sti¤ness matrix of an undistorted element generated by this class of methods.
