Matrix Methods of Structural Analysis
Presents the subject of advanced structural analysis in a wider perspective. The chapters have been completely rewritten, emphasizing the general view of structure as an assembly of truss, beam and finite elements. New additions introduce analytical methods of dynamic and nonlinear problems. Includes all the essential features of programming considerations required in developing computer programs of structural analysis.
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Displacement Method 11Finite Elements 257
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applied approach assembly assumed deformed axial load basic beam element beam model bending cantilever model Chapter coefficients computed Consider corresponding damping defined deformed shape degrees of freedom denote derived determined differential equation direction cosines displacement method distributed loads element deformations element forces element nodal element stiffness end forces equations of equilibrium equilibrium equations equilibrium relations equivalent nodal Example finite element method flexibility matrix flexibility relations force method force system Gauss given by Eq Hence internal forces iterative kinematic relations linear load vector mass matrix mode shapes nodal displacements nodal forces nodal loads nodes nonlinear numerical integration obtain plane frame plane stress plastic strain problems redundants rotation shape functions shearing deformation shown in Fig shows solution solving statics step stiffness matrix stiffness relations stress structural analysis subroutine truss element values virtual displacement virtual forces zero