A METHOD TO ANALYZE THE BEAM WITH DISTRIBUTED MATERIAL PROPERTIES

Since the element interpolation functions of a traditional beam element cannot rationally describe the displacement filed in a beam with variable material properties, inaccuracies will arise. A method to compute responses of a beam with distributed material properties is presented, which effectively avoids the limitation of traditional beam elements. The consistent equivalent nodal load and consistent mass matrix are derived for the presented beam element. Compared with the traditional beam element, higher accuracy of the presented element in the static analysis and eigenproblems is observed and the accurate internal element force and displacement fields can be modeled by only one element. This study provides a simple method and a useful theoretical basis for static and dynamic analyses of the beam with distributed material properties.