The stochastic equation of virtual work based on Total Lagrangian method is developed to analyze the influences of vicoelasticity, large deformation and randomness simultaneously. The nonlinear equilibrium equations of viscoelasticstochastic FEM are derived. The full Newton-Raphson method is used to get the numerical solutions.
Speclal solutions are given by the newlytyped method that three equilibrium equations have been reduced to a single 6th order partial differential equation.
After pointing out that the elastic coefficient at a node of a bar element with elastic joint is really a fuzzy quantity,the fuzzy stiffness matrix of the bar element is obtained,and a solution to structural fuzzy finite element equilibrium equations is presented.
In this article, the stability of bars subjected to compressible loads at multi points on its axis is investigated, the system of equilibrium equations in buckling configuration is derived, its general solution is given, and, finally, the nonlinear equation for critical load is obtained that is the generalization of Euler’s formula.
Based on the characteristics of the restrained finite element equilibrium equations in the analysisof the initial and bifurcate post-buckling behavior, the paper gives out a valuable method to change itto be non-restrained equations, and then the numerical example.
We use the principle of virtual displacements and the planar integration by parts to derive the geometrically nonlinear equilibrium equations and their boundary conditions of composite laminated plates depended on higher-order shear deformation theory in the form of five generalized displacements.
The construction method of homotopic differential equations and a new solution following curve algorithm are also given which succeed in calculation of the nonlinear equilibrium equations of aircraft.
This method uses the free torsional theory and the principle of virtual work to build governing equilibrium equations involving unknown shear flows and twisting rate.
There have been obtained system of equilibrium equations and recurrence relations for its coefficients which enable us to formulate the algorithm to build the system.
The level populations were determined by numerically solving the equation of recombination kinetics together with the statistical equilibrium equations for a 60-level model hydrogen atom.
Based on equilibrium condition,the system of combustion has mininum free energy.,The paper provides a new method that calculates the equilibtium composition of combustion products by penalty method.The method doesn't need differential and solve the matrix.There is no change of negative mol composition.The initial points don't demand to satisfy mass equilibrium equations.The paper givs an example,the results are satisfactory.
Based on the characteristics of the restrained finite element equilibrium equations in the analysisof the initial and bifurcate post-buckling behavior, the paper gives out a valuable method to change itto be non-restrained equations, and then the numerical example.
Present a quasi-static analytical model of rolling bearings in a multi-bearing shaft system with elastic deformation of the shaft. A stepped shaft in a commonly used shaft system is equivalently transformed into a smooth shaft. The displacements of each inner ring on the shaft can then be determined and the equilibrium equations of the shaft are taken as a set of basic equations for that system. In order to solve those non-linear algebraical equations with a number of unknowns,a nume...