In this paper, we introduced the random materials, geometrical shapes, force and displacement boundary condition directly into the functional variational formulations and developed a unified random variational princip...In this paper, we introduced the random materials, geometrical shapes, force and displacement boundary condition directly into the functional variational formulations and developed a unified random variational principle and finite element method with the small parameter perturbation method. Numerical examples showed that the methods have the advantages of the simple and convenient program implementation, and are effective for the random mechanics problems.展开更多
A second order explicit finite element scheme is given for the numerical computation to multi-dimensional scalar conservation laws.L p convergence to entropy solutions is proved under some usual conditions. For two-di...A second order explicit finite element scheme is given for the numerical computation to multi-dimensional scalar conservation laws.L p convergence to entropy solutions is proved under some usual conditions. For two-dimensional problems, uniform mesh, and sufficiently smooth solutions a second order error estimate inL 2 is proved under a stronger condition, Δt≤Ch 2/4展开更多
Based on the nonequilibrium thermodynamic theory, a new thermo-viscoelastic relation at finite strain is proposed. Under the assumption that the specific heat at a fixed strain and fixed internal variables can be rega...Based on the nonequilibrium thermodynamic theory, a new thermo-viscoelastic relation at finite strain is proposed. Under the assumption that the specific heat at a fixed strain and fixed internal variables can be regarded as a constant, a new expression for the free energy which decouples the mechanical and the thermal effects is derived. Through an analysis of the mesoscopic deformation mechanism of solid polymers, a set of internal variables is introduced, and an internal-variable consti-tutive theory in thermo-viscoelasticity at finite strain is formulated. An explicit expression of a thermo-viscoelastic constitutive relation is obtained for solid polymers in the case where their molecular network has a randomly oriented distribution function at reference configuration. Moreover, the relationship be-tween the relaxation time and the temperature is also discussed. The viscoelastic constitutive theory proposed in reference is only a linear approximation of the present theory.展开更多
文摘In this paper, we introduced the random materials, geometrical shapes, force and displacement boundary condition directly into the functional variational formulations and developed a unified random variational principle and finite element method with the small parameter perturbation method. Numerical examples showed that the methods have the advantages of the simple and convenient program implementation, and are effective for the random mechanics problems.
文摘A second order explicit finite element scheme is given for the numerical computation to multi-dimensional scalar conservation laws.L p convergence to entropy solutions is proved under some usual conditions. For two-dimensional problems, uniform mesh, and sufficiently smooth solutions a second order error estimate inL 2 is proved under a stronger condition, Δt≤Ch 2/4
文摘Based on the nonequilibrium thermodynamic theory, a new thermo-viscoelastic relation at finite strain is proposed. Under the assumption that the specific heat at a fixed strain and fixed internal variables can be regarded as a constant, a new expression for the free energy which decouples the mechanical and the thermal effects is derived. Through an analysis of the mesoscopic deformation mechanism of solid polymers, a set of internal variables is introduced, and an internal-variable consti-tutive theory in thermo-viscoelasticity at finite strain is formulated. An explicit expression of a thermo-viscoelastic constitutive relation is obtained for solid polymers in the case where their molecular network has a randomly oriented distribution function at reference configuration. Moreover, the relationship be-tween the relaxation time and the temperature is also discussed. The viscoelastic constitutive theory proposed in reference is only a linear approximation of the present theory.
