Finite element method Free Essay Example, 1000 words

Complex restraints can be handled and thus solutions to indeterminate structures can be provided by this method. Complex loading can be handled by this method as well. Instances are: frequency or time dependent loading, element load such as those obtaining from inertial forces, thermal or pressure as well as nodal load. (Weck and Kim Jan 21 2004, Slide 15) Disadvantages of Finite Element Method There are some disadvantages of this method as well. First of all, this method does not provide any general solution in closed form. Thus, one cannot examine responses of the system to changes in the defining parameters. Secondly, the solutions obtained are only approximate ones and not exact solutions. Therefore, predictions always are associated with some minute degree of error. Additionally, the models are associated with inherent errors. Finally, because of the gravity of the issues that typically use Finite Element analysis mistakes made by users or analysts can have literally fatal consequences. (Weck and Kim Jan 21 2004, Slide 16) The patch test 1) Definition The Patch test, originally created by Irons, is a simple numerically performable test to evaluate the validity of the formulation and programmed implementation of an element. We will write a custom essay sample on Finite element method or any topic specifically for you Only $17.96 $11.86/pageorder now The element is assumed to be stable and then if it passes the Patch test, it is taken as assurances for the fact that all necessary criteria for convergence are satisfied. Thus, if such an element is used for the purpose of modeling other structures, the process of mesh refinement generates an approximate solution sequence that converges to the exact solution. Therefore, this test serves the purpose of being both a necessary as well as sufficient condition for convergence of finite element formulations. (Cook, Malkus and Plesha 1989, 129) 2) Recommended procedure The basic procedure for a patch test is to use a microscope to approximate the actual structure which is being solved with an extremely fine mesh. A patch of minute elements as well as a little region belonging to the real structure should be visible. Provided this region is adequately small, the observed stresses are sensibly constant. Thus, this patch of minute elements is expected to serve as a model for the constant stress. The patch test constitutes of the following recommended steps: a) We initialize the process by taking an arbitrary geometry of the patch of elements. The test is successful if a match up to 6 decimals is obtained and it fails otherwise. Based on one test, it is asserted that the process would be successful for all other geometries as well.