| Popis: |
This paper gives continuation of geometric nonlinear analysis presented in former papers. Phenomenons of snap-through and snap-back can occur during nonlinear analysis of shallow arches, for specific geometries and loadings. Considering that throughout this complex equilibrium paths structure can reach both loading and displacement limit points, classical Newton-Raphson schemes based only on loading or displacement control are no longer applicable. Arc-length method for plane frames is presented here in order to describe this phenomenons with the usage of classical Bernoulli-Euler beam element. Calculation is made using the total Langrangian approach. Vector of unbalanced forces and tangent stiffness matrix are derived in its closed-form, which significantly saves calculation time usually required for numerical integration. Special attention is paid to determination of sign of predictor solution at the beginning of each increment. Presented approach is programmed into Wolfram Mathematica. Detailed numerical example is given at the end. Comparison of results obtained with presented approach and the ones from commercial FEM software Abaqus is given. |
