Transcription of Chapter 10 – Isoparametric Elements - Memphis
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Chapter 10 – Isoparametric Elements - Memphis
Chapter 10 Isoparametric ElementsLearning Objectives To formulate the Isoparametric formulation of thebar element stiffness matrix To present the Isoparametric formulation of theplane four-noded quadrilateral (Q4) elementstiffness matrix To describe two methods for numericalintegration Newton-Cotes and GaussianQuadrature used for evaluation of definiteintegrals To solve an explicit example showing theevaluation of the stiffness matrix for the planequadrilateral element by the four-point Gaussianquadrature ruleChapter 10 Isoparametric ElementsLearning Objectives To illustrate by example how to evaluate thestresses at a given point in a plane quadrilateralelement using Gaussian quadrature To evaluate the stiffness matrix of the three -nodedbar using Gaussian quadrature and compare theresult to that found by explicit evaluation of thestiffness matrix for the bar To describe some higher-order shape functions forthe
Step 3 -Strain-Displacement and Stress-Strain Relationships Recall that use of linear shape functions results in a constant [B] matrix, and hence, in a constant strain within the element. For higher-order elements, such as the quadratic bar with three nodes, [B] becomes a function of natural coordinates s.
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