FEA Short Course

PLANE STRESS AND PLANE STRAINSimplified Elasticity FormulationsDisplacement FormulationEliminate the stresses and strains from the general system of equations. This generates a system of three equations for the three unknown displacement components. Stress FormulationEliminate the displacements and strains from the general system of equations. This generates a system of six equations and for the six unknown stress components. The General System of Elasticity Field Equationsof 15 Equations for 15 Unknowns Is Very Difficultto Solve for Most Meaningful Problems, and So Modified Formulations Have Been Developed.Solution to Elasticity ProblemsF(z)G(x,y)zx yEven Using Displacement and Stress FormulationsThree-Dimensional Problems Are Difficult to Solve!So Most Solutions Are Developed for Two-Dimensional ProblemsTwo and Three Dimensional ProblemsxyzxyzThree-DimensionalTwo-DimensionalxyzSpherical CavityTwo-Dimensional FormulationxyzRxyzR2hPlane StrainPlane Stress