Matrix Methods of Structural Analysis |
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a₁ a₂ applied approach assembling assumed axial b₁ b₂ basic beam element beam model C₁ C₂ cantilever model coefficients computed Consider coordinates corresponding damping degrees of freedom derived determined displacement method distributed loads elastic element stiffness end forces equations of equilibrium Example finite element finite element method freedom system Gauss given by Eq Hence internal forces iteration K₁ k₂ kinematic linear load increment load vector M₁ M₂ mass matrix mode shapes multi-degree N₁ N₂ nodal forces nodes nonlinear numerical integration NUMGP obtain On+1 P₁ P₂ plane strain plane stress problems redundants S₁ scheme shape functions shearing shown in Fig shows solution solving stiffness matrix stiffness relations stress-strain stress-strain curve structural analysis SUBROUTINE transformation truss element u₁ u₂ V₁ v₂ values virtual virtual displacements yield condition zero ΕΙ дх