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Amplitude of specified Arch Under Central Beam on Nonlinear bifurcation calculation of limit CM rO CM coefficients curve direct iteration scheme element idealization consisting element stiffness equations element structural analysis Equation 11 Equation 3a EQUILIBRIUM EQUATIONS exact solution exhibit a snap-through extrapolation and imposition finite element concept foundation modulus geometric stiffness matrices governing algebraic equations governing equations derive HINGED SHALLOW ARCH indicial notation initial displacements iterative method joint of beam Knee-Frame Koiter Limit load intensity LIMIT POINT CALCULATION limit point load linear prebuckling linear stiffness matrix Load-Displacement Behavior Load-Displacement Plot NijkA Nonlinear analysis Nonlinear Elastic Foundation Nonlinear Foundation nonlinear load-displacement path number of terms Oí Oí Performing Organization perturbation method post-buckling present method prior load level Reference 11 Security Classif shown in Figure snap-through buckling solution point solved in illustration Spring constants Taylor series test data tion total stiffness matrix vector and component