We investigate primal and mixed u−p isogeometric collocation methods for application to nearly-incompressible isotropic elasticity.The primal method employs Navier’s equations in terms of the displacement unknowns,an...We investigate primal and mixed u−p isogeometric collocation methods for application to nearly-incompressible isotropic elasticity.The primal method employs Navier’s equations in terms of the displacement unknowns,and the mixed method employs both displacement and pressure unknowns.As benchmarks for what might be considered acceptable accuracy,we employ constant-pressure Abaqus finite elements that are widely used in engineering applications.As a basis of comparisons,we present results for compressible elasticity.All the methods were completely satisfactory for the compressible case.However,results for low-degree primal methods exhibited displacement locking and in general deteriorated in the nearly-incompressible case.The results for the mixed methods behaved very well for two of the problems we studied,achieving levels of accuracy very similar to those for the compressible case.The third problem,which we consider a“torture test”presented a more complex story for the mixed methods in the nearly-incompressible case.展开更多
基金FF and LDL gratefully acknowledge the financial support of the German Research Foundation(DFG)within the DFG Priority Program SPP 1748“Reliable Simulation Techniques in Solid Mechanics”.AR has been partially supported by the MIUR-PRIN project XFAST-SIMS(No.20173C478 N).
文摘We investigate primal and mixed u−p isogeometric collocation methods for application to nearly-incompressible isotropic elasticity.The primal method employs Navier’s equations in terms of the displacement unknowns,and the mixed method employs both displacement and pressure unknowns.As benchmarks for what might be considered acceptable accuracy,we employ constant-pressure Abaqus finite elements that are widely used in engineering applications.As a basis of comparisons,we present results for compressible elasticity.All the methods were completely satisfactory for the compressible case.However,results for low-degree primal methods exhibited displacement locking and in general deteriorated in the nearly-incompressible case.The results for the mixed methods behaved very well for two of the problems we studied,achieving levels of accuracy very similar to those for the compressible case.The third problem,which we consider a“torture test”presented a more complex story for the mixed methods in the nearly-incompressible case.
