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Numerical Advanced Computer Aided Engineering

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Added on  2020-02-24

Numerical Advanced Computer Aided Engineering

   Added on 2020-02-24

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Numerical1 | P a g eAdvanced Computer Aided Engineering
Numerical Advanced Computer Aided Engineering_1
NumericalContentsSolution-1).......................................................................................................................................3Solution-2).......................................................................................................................................5Solution-3).......................................................................................................................................7Solution-3a1)...............................................................................................................................7Solution-3aii)...............................................................................................................................8Solution-3aiii)..............................................................................................................................8Solution-3B)................................................................................................................................92 | P a g e
Numerical Advanced Computer Aided Engineering_2
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=Whereσ=[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=E1ν2 , E2=νE1Whereas for plane strainE1=E(1ν)(1ν)(1+ν)E2=νE1(1ν)The element stiffness relation is given by Ku=FWhere k is stiffness and3 | P a g e
Numerical Advanced Computer Aided Engineering_3

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