Transcription of Chapter 9 – Axisymmetric Elements - Memphis
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Chapter 9 – Axisymmetric Elements - Memphis
Chapter 9 Axisymmetric ElementsLearning Objectives To review the basic concepts and theory ofelasticity equations for Axisymmetric behavior. To derive the Axisymmetric element stiffnessmatrix, body force, and surface traction equations. To demonstrate the solution of an axisymmetricpressure vessel using the stiffness method. To compare the finite element solution to an exactsolution for a cylindrical pressure vessel. To illustrate some practical applications ofaxisymmetric ElementsIntroductionIn previous chapters, we have been concerned with line or one-dimensional Elements (Chapters 2 through 5) and two-dimensional Elements (Chapters 6 through 8). In this Chapter , we consider a special two-dimensional element called the Axisymmetric element is quite useful when symmetry with respect to geometry and loading exists about an axis of the body being analyzed.
The tangential strain is due only to the radial displacement. Having only radial displacement u, the new length of the arc AB is (r + u)d , and the tangential strain is then given by: rud rd rd u r CIVL 7/8117 Chapter 9 - Axisymmetric Elements 9/66
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