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Basic And Shape Sensitivity Tests For Membrane And Plate Bending Finite Elements

Basic And Shape Sensitivity Tests For Membrane And Plate Bending Finite Elements


Due to the evolving nature of the engineering analysis and simulation market this publication no longer represents current best practice and has been archived. The document may be of historical interest and is therefore still available for purchase






This report presents basic and shape sensitivity tests for membrane and plate bending elements. The basic tests cover element completeness and the shape sensitivity tests investigate the effects of element aspect ratio, skew and taper. There is no restriction on the number of element nodes and the tests cover both quadrilaterals and triangles.

A set of shape parameters for a quadrilateral/triangle are defined and a new and general method of element testing is presented and referred to as the "CRE-Method". Membrane and plate bending continuum elasticity solutions are given for comparison with finite element results


Contents 

Chapter 1 The CRE Method


Chapter 2 Shape Parameters

  • The Quadrilateral
    • Aspect Ratio
    • Skewness
    • Taper
  • The Triangle
    • Aspect Ratio
    • Skewness


Chapter 3 Membrane Continuum Elasticity Solutions

  • Zero Stress
  • Constant Direct Stress (σ x)
  • Constant Direct Stress ( σ y)
  • Constant Shear Stress (τ xy)
  • Constant Moment
  • Linear Moment
  • A program For Membrane Elasticity Solutions


Chapter 4 Membrane Boundary Loadings

  • Loadings Normal and Tangential to Boundary
  • Boundary Loadings in Cartesian System
  • A program for Boundary Loadings


Chapter 5 Replacing Distributed Loadings with Equivalent Forces

Chapter 6 Single Element Completeness Tests for Membranes

  • Quadrilateral Elements
    • Rigid Body Mode Test
    • Constant σ x Test
    • Constant σ y Test
    • Constant τ xy  Test

  • Triangular Elements 
    • Rigid Body Mode Test
    • Constant σ x Test
    • Constant σ y Test
    • Constant τ xy  Test


Chapter 7 Completeness Test for an Assemblage of Membrane Elements (Patch Test)


Chapter 8 False Zero Energy Mode Tests for membranes

  • Iterative-type Procedure
  • Eigenvalue Procedure


Chapter 9 Invariance Tests For Membranes


Chapter 10 Shape SensitivityTEsts for Membranes

  • The Continuum Loadings
  • Nodal Coordinates in Terms of Shape Parameters
  • A program for Nodal Coordinates
  • Aspect Ratio Sensitivity
  • Skew Sensitivity 
  • Taper Sensitivity
  • Skew Sensitivity for Differing Aspect Rations
  • Taper Sensitivity for Differing Aspect Ratios
  • Combined Sensitivities
  • Which are the Best Membranes Elements?


Chapter 11 Plate Bending Continuum Elasticity Solutions

  • Zero Moments
  • Constant Bending Moment (Mx)
  • Constant Bending Moment (My)
  • Constant Twisting Moment (Mxy)
  • Linear Bending Moment (Mx)
  • A program for Plate Bending Elasticity Solutions


Chapter 12 Plate Boundary Loadings

  • Two Moments And A Shear
  • Kirchhoff Loads
  • A program for Boundary Loadings


Chapter 13 Replacing Distributed Loadings with Equivalent Forces

Chapter 14 Single Element Completeness Tests for Plates

  • Quadrilateral Elements
    • Rigid Body Mode Test
    • Constant Mx Test
    • Constant My Test
    • Constant Mxy Test

  • Triangular Elements
    • Rigid Body Mode Test
    • Constant Mx Test
    • Constant My Test
    • Constant Mxy Test

Chapter 15 Completeness Test for  an Assemblage of Plate Bending Elements (Patch Test)


Chapter 16 False Zero Energy Mode Test for Plates


Chapter 17 Invariance tests for plates


Chapter 18 Shape Sensitivity Tests for Plates

References



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About

J. Robinson

First Published: 1985

Softback, 32 pages