Defense Technical Information Center (DTIC) · 1979 · 111 citations · 0 references
ComputingCivil EngineeringComputational EngineeringComputational Structural AnalysisFinite Element AnalysisFinite Element MethodsAdaptive Mesh RefinementError EstimationFinite Element FormulationNonlinear Finite Element AnalysisNonlinear Structural AnalysisStructural Finite Element AnalysisAccuracy-computational Cost TradeoffComputational Structural MechanicsError Estimation For Finite Element SolutionsEstimation ErrorFinite Element ModelingFinite-element Mesh AdaptationMesh AdaptationMesh Adaptation Criteria
The finite element method has become a powerful tool for solving a broad range of problems in computational structural analysis and design. This report seeks to compute reliable error estimates for finite element solutions at reasonable cost and to design solution processes that achieve prescribed accuracy or optimal cost‑efficiency. The study first examines one‑ and two‑dimensional problems before extending the results to nonlinear cases. Experimental results on a nonlinear two‑point boundary‑value problem demonstrate that combining continuation, error estimation, and adaptive mesh construction yields an extremely effective computational approach for many engineering problems. The report contains 15 figures and 11 tables.
Recent work in computational structural analysis and design has been greatly aided by the evolution of the finite element method into a powerful tool for the solution of a broad range of problems. This report addresses the following questions: how to calculate, at reasonable cost, reliable estimates of the error of computed finite element solutions; how to set up the overall solution process so as to achieve, with reasonable certainty and efficiency, a solution for which the accuracy either falls into a prescribed range or is best possible for the allotted computational cost. Certain one- and two- dimensional problems are considered first; later, the results are extended to nonlinear problems. Experimental results for a particular nonlinear two-point boundary-value problem show that the combination of continuation, error estimation, and adaptive mesh construction should be an extremely effective approach to the computational solution of many practical engineering problems. 15 figures, 11 tables. (RWR)