Solving the Stress Problem for a Finite Cylinder by the Schwarz Method with Hybrid Approximations

An axisymmetric elastic problem is solved by a heterogeneous numerical scheme of the alternating Schwarz method based on the finite- and boundary-element methods. The Schwarz method and the modified scheme are compared. A relaxation parameter is used to accelerate the iterative process     

Domain decomposition methods applied to solve frictionless-contact problems for multilayer elastic bodies

A parallel Dirichlet–Dirichlet domain-decomposition algorithm for solving frictionless-contact problems for elastic bodies made of composite materials is proposed and justified. Numerical results that demonstrate the effectiveness of the approach and its software implementation are presented     

Solution of three-dimensional problems on the free vibration of axisymmetric bodies

S. P. Timoshenko Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Lvov University. Translated from Prikladnaya Mekhanika, Vol. 30, No. 5, pp. 19–23, May, 1994.     

Convergence of the Neumann parallel scheme of the domain decomposition method for problems of frictionless contact between several elastic bodies

Based on the variational formulation and penalty method, we have considered the Neumann parallel scheme of the domain decomposition method for the solution of problems of one-sided contact between three-dimensional elastic bodies. We have shown the existence and uniqueness of a solution of the variational problem with penalty and convergence in the penalty parameter. The convergence of this scheme has been proved, and the optimal value of iteration parameter has been determined.     

Influence of Anisotropy on the Response Characteristics of Finite Cylinders Under Free Vibrations

A numerical–analytical approach is proposed to solve a problem on the free vibrations of cylindrical bodies. The approach is based on three-dimensional elastic theory and the semianalytic finite-element method. The free vibrations of isotropic and anisotropic solid cylinders of finite length are examined. It is studied how boundary conditions and mechanical and geometrical parameters affect the distribution of dynamic properties. The efficiency of the approach proposed is tested by comparing results produced by different approaches