A Method of Limit Point Calculation in Finite Element Structural Analysis, Issue 2115An approach is presented for the calculation of limit points for structures described by discrete coordinates, and whose governing equations derive from finite element concepts. The nonlinear load-displacement path of the imperfect structure is first traced by use of a direct iteration scheme and the determinant of the governing algebraic equations is calculated at each solution point. The limit point is then established by extrapolation and imposition of the condition of zero slope of the plot of load vs. determinant. Three problems are solved in illustration of the approach and in comparison with alternative procedures and test data. |
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... section is to define the general algebraic form of finite element stiffness equations for the present geometrically nonlinear analysis . The term " finite element stiffness equations " implies that the elas- tic deformational behavior ...
... section is to define the general algebraic form of finite element stiffness equations for the present geometrically nonlinear analysis . The term " finite element stiffness equations " implies that the elas- tic deformational behavior ...
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... Section IV . These results , ex- pressed as a percentage of the Reference 13 solution , are listed in Table 2. The results are comparable in accuracy with the limit point load results and are quite acceptable at or beyond the 92 % point ...
... Section IV . These results , ex- pressed as a percentage of the Reference 13 solution , are listed in Table 2. The results are comparable in accuracy with the limit point load results and are quite acceptable at or beyond the 92 % point ...
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... ( Section 158 Postal Manual ) Do Not Return " The aeronautical and space activities of the United States shall be conducted so as to contribute ... to the expansion of human knowl- edge of phenomena in the atmosphere and space . The ...
... ( Section 158 Postal Manual ) Do Not Return " The aeronautical and space activities of the United States shall be conducted so as to contribute ... to the expansion of human knowl- edge of phenomena in the atmosphere and space . The ...
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2Nijk A-Det Amplitude of specified Arch Under Central b₁ b₂ Beam on Nonlinear bifurcation calculation of limit coefficients curve direct iteration scheme element idealization consisting element stiffness equations element structural analysis Equation 11 Equation 3a EQUILIBRIUM EQUATIONS exhibit a snap-through extrapolation and imposition Extrapolation Method finite element structural foundation modulus governing algebraic equations HINGED SHALLOW ARCH I-III Imperfection Amplitude indicial notation initial displacements iterative method Iterative Solution Points joint of beam k₁ k₂ k₂w² Knee-Frame Koiter Limit load intensity LIMIT POINT CALCULATION limit point load linear prebuckling N₁ N₂ Nijke Nonlinear analysis Nonlinear Elastic Foundation Nonlinear Foundation nonlinear load-displacement path number of terms Performing Organization Perturbation Method Ref Post-Buckling Path present method prior load level Reference 11 Security Classif shown in Figure solved in illustration Spring constants Taylor series test data tion total stiffness matrix vector and component Womax Δ Δ