Introduction to the Finite Element Method; a Numerical Method for Engineering Analysis

applications approach approximate ASCE assemblage assumed axisymmetric b₁ b₂ basic beam behavior body boundary conditions Chapter computed consider coordinate system curve deformation degrees of freedom derived direct stiffness method discretization displacement method displacement model elastic elastic-plastic element stiffness engineering equilibrium equations example external nodes field variable finite element analysis finite element method fluid geometric incremental procedure integration interpolation model isoparametric iterative linear linear elastic load vector mesh modulus natural coordinate nodal displacements nodal points nonlinear analysis obtain parameters plane strain plane stress plastic plate bending Poisson's ratio polynomial potential energy Proc quadratic quadrilateral Reference rock mechanics Sample Problem Section seepage shear shell shown in Figure soils and rocks solid mechanics stiffness and load stiffness matrix strain-displacement Stress Analysis stress-strain stress-strain curve structure surface symmetric technique theory three-dimensional triangle triangular element two-dimensional u₁ variational principle Zienkiewicz ди ду дх