Semi-analytical method of finished elements in elastic and elastic-plastic position for curviline prismatic objects
Keywords:finite element method, semi-analytical finite element method, block iteration method, linear and nonlinear equations, elastic and elastic-plastic deformation, Michlin polynomials, curvilinear prismatic bodies
In [4, 5, 6] the algorithm of the method of block iterations of solving linear and nonlinear equations by the semivanalytic finite element method for curvilinear inhomogeneous prismatic bodies is realized. This paper presents the results of the effectiveness of the semi-analytical finite element method for the consideration of curvilinear prismatic objects in elastic and elastic-plastic formulation.
The choice of the optimal in terms of machine time and speed of convergence of the iterative process algorithm for solving systems of linear and nonlinear equations by the semivanalytic finite element method [1, 2, 3] is an important factor influencing the efficiency of the method as a whole. Numerous studies have shown that using the block iteration method to solve systems of equations of the semivanalytic finite element method for prismatic bodies with variable parameters has a number of important advantages over solving systems of the traditional variant of the finite element method.
The organization of the computational process and its software implementation takes into account the basic requirements for software for calculating strength on modern software packages. The modular structure of the developed system of programs provides its non-closedness concerning new classes of tasks.
The use of the block iteration method to solve systems of nonlinear equations of SAFEM is approximately an order of magnitude superior to the traditional finite element method.
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