Matrix Methods of Structural Analysis |
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a₁ a₂ applied approach assembling assumed axial b₁ b₂ basic beam element C₁ C₂ cantilever model coefficients computed Consider coordinates corresponding damping deformations degrees of freedom derived determined displacement method distributed loads Duhamel Integration dynamic elastic element stiffness equations of equilibrium equivalent nodal Example finite element method flexibility freedom system Gauss given by Eq global stiffness Hence internal forces iterative K₁ k₂ kinematic linear load increment load vector M₁ M₂ mass matrix mode shapes multi-degree N₁ N₂ nodal forces NODEL nodes nonlinear numerical integration NUMGP obtain P₁ P₂ plane strain plane stress plastic strain problems S₁ scheme shape functions shown in Fig shows solution solving static step stiffness matrix stiffness relations strain increment stress-strain structural analysis SUBROUTINE tangent stiffness truss element u₁ u₂ v₁ v₂ values virtual virtual displacements zero