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 three-noded linear strain bar, the improvedbilinear quadratic (Q6), the eight- and nine-nodedquadratic quadrilateral (Q8 and Q9) Elements , andthe twelve-noded cubic quadrilateral (Q12)

Step 3 -Strain-Displacement and Stress-Strain Relationships To construct the element stiffness matrix, determine the strain, which is defined in terms of the derivative of the displacement with respect to x. The displacement u, however, is now a function of s so we must apply the chain rule of differentiation to the function u as follows: du du dx

Loading..

Tags:

  Displacement, Strain

Information

Related search queries