Let us plot out this function, and keep in mind that we are trying to find u such that f(u)=0.įinding the solution to the problem is, in fact, only marginally different from the linear case. In this case, only the spring stiffness is dependent on the solution, but more generally, both the load and the properties of the elements can be arbitrarily dependent upon the solution in a nonlinear problem. Just as we did earlier for the linear problem, we can now write the following function describing the balance of forces on the node for the nonlinear finite element problem: We are interested in finding the displacement of the end of the spring, where the force is applied. That is, the spring stiffness increases exponentially as it is stretched. The stiffness of the spring is a function of the distance it is stretched, k(u)=exp(u). This information is presented in the context of a very simple 1D finite element problem, and builds upon our previous entry on Solving Linear Static Finite Element Models.Įditor’s note: The information in this blog post is superseded by this Knowledge Base entry: “ Improving Convergence of Nonlinear Stationary Models” A System of a Spring Attached to a Rigid WallĬonsider the system shown below, of a spring that is attached to a rigid wall at one end, and with an applied force at the other end.
Here, we begin an overview of the algorithms used for solving nonlinear static finite element problems.
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