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 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)
uniform over the perimeter and along the length of the element, we obtain: where we now assume {Tx}is in units of force per unit length. Isoparametric Elements Isoparametric Formulation of the Bar Element Step 4 -Derive the Element Stiffness Matrix and Equations Since {Tx}is in force-per-unit-length {Tx}L is now the total force.
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