Introduction to Finite Element Analysis

Posted on 01 Jun 2020 04:25 pm

Analytical Solution • Stress analysis for trusses, beams, and other simple structures are carried out based on dramatic simplification and idealization: – mass concentrated at the center of gravity – beam simplified as a line segment (same cross-section) • Design is based on the calculation results of the idealized Interpolation Functions for General Element Formulation In finite element analysis, solution accuracy is judged in terms of convergence as the element “mesh” is refined. There are two major methods of mesh refinement. In the first, known as h-refinement, mesh refinement refers to the process of increasing the number of elements used to model a given domain, consequently, reducing individual element size. In the second method, p-refinement, element size is unchanged but the order of the polynomials used as interpolation functions is increased. The objective of mesh refinement in either method is to obtain sequential solutions that exhibit asymptotic convergence to values representing the exact solution. structure & a large safety factor (1.5-3) given by experience. FEA • Design geometry is a lot more complex; and the accuracy requirement is a lot higher. We need – To understand the physical behaviors of a complex object (strength, heat transfer capability, fluid flow, etc.) – To predict the performance and behavior of the design; to calculate the safety margin; and to identify the weakness of the design accurately; and – To identify the optimal design with confidence