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array back-substitution beam element boundary calculate CALL DOCTOR central node chapter coefficients column CONTINUE coordinates corner nodes d(area derivatives diagnostics diagonal eigenvalues ELSTIF engineering equations errors example Exercise finite element forces formulation FORTRAN front solution frontwidth GASH Gauss give iso-P elements JPROP linear LNODS LNODZ LNOMAX Loof nodes LPOP LTYPE LVABZ LVMAX MAXTRS membrane mesh midside nodes NDIM NELZ NEWRHS NEXTIF NLOOF nodal deflections nodal line nodal loads nodal variables node number NODFIX NODMAX normal NSTAGE numerical integration NVEC patch test pivot plane strain plane stress plate bending Poisson's ratio potential energy problem quadratic re-solution right-hand sides rigid body motions rotations roundoff scalar scalar product Section Semiloof shape function constraints shear shear stresses slope stiffness matrix storage strain energy structure subroutine Taig quadrilateral technique tetrahedra theorem thickness triangle values vector VPROP WCORN WLOOF WSHEL Young's modulus zero