V.V. Zozulya¹

CMES-Computer Modeling in Engineering & Sciences, Vol.42, No.3, pp. 187-216, 2009, DOI:10.3970/cmes.2009.042.187

Abstract The mathematical statement for contact problem with unilateral restrictions and friction is done in classical and weak forms. Different variational formulation of unilateral contact problems with friction based on principles of virtual displacements and virtual stresses are considered. Especially boundary variational functionals that are used with boundary integral equations have been established. Nonsmooth optimization algorithms of Udzawa type for solution of unilateral contact problem with friction have been developed. Some theoretical results of existence and uniqueness in elastostatic unilateral contact problem with friction are outlined. More >

Shang Zhang^{1, *}, Seyedmehdi Karimi², Shahaboddin Shamshirband^{3, 4, *}, Amir Mosavi^5,6

CMC-Computers, Materials & Continua, Vol.58, No.2, pp. 567-583, 2019, DOI:10.32604/cmc.2019.02795

Abstract In the process of eliminating variables in a symbolic polynomial system, the extraneous factors are referred to the unwanted parameters of resulting polynomial. This paper aims at reducing the number of these factors via optimizing the size of Dixon matrix. An optimal configuration of Dixon matrix would lead to the enhancement of the process of computing the resultant which uses for solving polynomial systems. To do so, an optimization algorithm along with a number of new polynomials is introduced to replace the polynomials and implement a complexity analysis. Moreover, the monomial multipliers are optimally positioned to multiply each of the… More >

G. Gang¹, Y.H. Liu²

CMC-Computers, Materials & Continua, Vol.20, No.3, pp. 251-272, 2010, DOI:10.3970/cmc.2010.020.251

Abstract Limit and shakedown analysis theorems are the theories of classical plasticity for the direct computation of the load-carrying capacity under proportional and varying loads. Based on Melan's theorem, a solution procedure for lower bound limit and shakedown analysis of three-dimensional (3D) structures is established making use of the finite element method (FEM). The self-equilibrium stress fields are expressed by linear combination of several basic self-equilibrium stress fields with parameters to be determined. These basic self-equilibrium stress fields are elastic responses of the body to imposed permanent strains obtained through elastic-plastic incremental analysis by the three-dimensional finite element method (3D-FEM). The… More >