Some fundamental problems of nonlinear finite elements are presented, which include some fundamental concepts on strain, stress and nonlinear equilibrium equation, and geometrical nonlinear finite elements of displacement model, hybrid model and quasi-conforming model based on different nonlinear geneialized variational principles, and its application in buckling of shell.
In the present paper, the nonlinear differential equations and stability equations for slender toroidal shells are derived from Sander' s nonlinear equilibrium equations and Koiter's compatibility equations for small strains.
The nonlinear equilibrium equations and geometrical relations of axially symmetrical toroidal shells are derived under the assumption of the little deformation ε<<1, the moderate rotation β<1 and .
The volume integrals are integrated numerically using Gauss quadrature, and the resulting nonlinear equilibrium equations are solved by Newton-Raphson incremental-iterative procedures.
Similarly, we also establish existence results for those nonlinear equilibrium problems which may be transfered to the system of generalized vector quasi-equilibrium problems.
After deriving the stochastic constitutive relations between the second Piola-Kirchhoff stress tensor and Green strain tensor, the nonlinear viscoelastic stochastic finite element formulae were put forward. The Newton-Raphson iterative method was used for the solution of the nonlinear equilibrium equations. The combined influence of viscoelasticity, geometrically nonlinearity and randomness could be investigated using the innovated method.
In this paper, we establish that the nonlinear equilibrium equation for this model has nontrivial solutions which appear for critical values of the pressure.
When a weak forcing is balanced with a weak dissipation, two (linear and nonlinear) equilibrium states can be produced, depending on the initial condition.
It is proposed that the zonally asymmetric forcing and the nonlincarity of horizontal advection are the two essential factors in the mechanism of blocking. This idea is numerically tested with a quasi-geostrophic, two level spectral model including the effect of asymmetric diabatic heating. The results show that a stably maintained blocking pattern will be created only when the two factors are included simultaneously. The blocking pattern does not occur when either of two factors is omitted. The effect of i...
Buckling is one of many complex topics in structural mechanics. The analytical solutions can be obtained only in a few cases. In recent years a great deal of attention has been concentrated on the nonlinear finite-element method to analyze the stability of structures, especially nonlinear stability. Most of the finite element analyses of stability are based on perturbation technique or incremental/iterative approach. The perturbation technique is restricted to linear prebuckling path and immedia...
Some fundamental problems of nonlinear finite elements are presented, which include some fundamental concepts on strain, stress and nonlinear equilibrium equation, and geometrical nonlinear finite elements of displacement model, hybrid model and quasi-conforming model based on different nonlinear geneialized variational principles, and its application in buckling of shell.