Algorithms analysis for solving geometrically nonlinear mechanics problems in the scheme of the semi-analytical finite element method

The effectiveness of using the semi-analytical finite element method (SAFEM) to research geometrically nonlinear construction mechanics problems for 3D bodies revolution under arbitrary loads based on a basic ring is considered. An estimate rational application parameters algorithms taking into account geometric nonlinearity defined above structures class, which has been obtained.
 In process numerically solving spatial theory elasticity and plasticity with displacements, choice systems equations fundamental importance. It conditioned by need determining coordinates discrete model in actual configuration changing metric characteristics elements, which, its turn, leads necessity multiple solutions high order. Due introduction additional hypotheses that do not reduce accuracy approximation: representation deformations stresses physical terms accordance moment scheme (MSFEM), it possible, one hand, avoid time-consuming procedure numerical integration over cross-sectional area element, other hand- maintain efficiency discretization. important stage implementation computer selection optimal, from point solution convergence speed equilibrium equations. specificity algebraic SAFEM violation trigonometric function orthogonality space operator variable stiffness mass along guide. clearly block structure matrix became basis combining direct iterative methods solving. reliability obtained results approach are confirmed wide range control examples various boundary conditions external loads.