Finite-element modeling of critical loads of buckling of structures considering of nonlinearity of pre-buckling state

Abstract

Abstract An approach is proposed to determine the critical loads of buckling, taking into account the geometric nonlinearity of the subcritical stress-strain state of structures. The first stage involves the structure strain-stress state in the context of geometrical non-linearity at some preset loading level. Afterwards the found solution neighborhood is supplemented with linearized non-linear equation system and the solution for the obtained linearized system is found. Following is the second linearization of the initial equation system in the linearized system solution neighborhood, obtained at the previous stage. The condition of equation systems degeneracy obtained after the second linearization causes a generalized eigenvalue problem. The approach is implemented using finite element models for the calculation of shell structural elements.