2d plane elastic problems
DESCRIPTION
elastic problemsTRANSCRIPT
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2D PLANE ELASTIC PROBLEMSPlane stress problem.Plane strain problem.
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Stress strain relationship i.e., constitutive matrix [D] for plane strain analysis
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Strain displacement relationships used in 2D plane elastic problem
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Formulation of characteristic equation for 2D plane stress/strain problemUsually the derivation of element equation for stress analysis is derived by Energy method Virtual displacementElement equation by energy method
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i.e., Change in internal energy=change in external energyThis can be written in matrix form
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The external work done is created by body force (density), surface traction (pressure)and by point load
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Now , the displacement vector field can be defined in 2D elastic problem:If triangular element is used the equation (7) can be expanded as Similarly if rectangular element is used
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Formation of characteristic equation for stress analysis including residual stress and residual strain
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Shape function of a 3 node triangular element (CST) constant strain triangular elementkji
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Writing above equations in matrix form
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And in turn
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Derivation of element equation of a 3 node triangular element for plane stress/plane strain analysis
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