Numerical1 | P a g eAdvanced Computer Aided Engineering
NumericalContentsSolution-1).......................................................................................................................................3Solution-2).......................................................................................................................................5Solution-3).......................................................................................................................................7Solution-3a1)...............................................................................................................................7Solution-3aii)...............................................................................................................................8Solution-3aiii)..............................................................................................................................8Solution-3B)................................................................................................................................92 | P a g e
NumericalSolution-1)As given in question,The problem is about first order fournode rectangular elements.To solve this problem we have toassume that the figure depicts stresscondition are similar to those of twodimensional plane elasticity.Therefore, the stress/ strainrelationship is given byσ=DεWhereσ=[σxσyτxy]Tε=[εxεyγxy]TAs we know that for an isotropic material, the stress strain D matrix is D=[E1E2OE2E1OOOG]Where the shear modulus is given by G=E2(1+ν)Where, E = Young’s Modulus and ν denotes Poisson’s ratio.For plane stress: E1=E1−ν2 , E2=νE1Whereas for plane strainE1=E(1−ν)(1−ν)(1+ν)E2=νE1(1−ν)The element stiffness relation is given by Ku=FWhere k is stiffness and3 | P a g e
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