Journal of the Engineering Mechanics Division · 1972 · 10 citations · 0 references
Natural SciencesComputational EngineeringMathematicsComputational MechanicsFinite Element AnalysisFinite Element MethodsComputational Solid MechanicsFinite Element DiscretizationNonlinear ProgrammingPlastic AnalysisPlastic DeformationQuadratic ProgrammingComputational PlasticityElastoplasticityFinite Element Methods In ElasticityFinite Element ModelingFinite Element SimulationPlasticity AnalysisPrinciple Of Minimum Total Complementary EnergySolid Mechanics Formulation
The plastic principles of absolute minimum of the rate of total potential energy and total complementary potential are used as tools for fomulating the elastic-plastic analysis of various types of structures as a problem in nonlinear programming. The finite element technique is used to discretize a continuum and thus obtain an admissible field in terms of a finite number of parameters. For an elastic-perfectly plastic material it is shown that a force formulation has a definite advantage in that the knowledge whether a plastic element unloads or remains plastic becomes unnecessary and the problem can be formulated as a quadratic programming problem. Numerical examples illustrate the solution technique.