Measuring the convergence behavior of shell analysis schemes

Abstract

a b s t r a c tWhile shells have been analyzed abundantly for many years in engineering and the sciences, improved finite element and related analysis methods are still much desired and researched. More general and effective finite element procedures are needed for complex shell structures, including for the analysis of composite shells and the optimization of shells. In this paper we discuss how finite element methods, and other analysis techniques, should be tested in order to identify their reliability and effectiveness. We summarize some important theoretical results, present appropriate test problems and convergence measures, and we illustrate our discussion through some novel numerical results. An important conclusion is that the testing has to be performed very carefully in order to obtain relevant results, and we show how this is accomplished in detail.

Improved stresses for the 4-node tetrahedral element

“…For example, if the structure is thin in one direction and long in the other two directions a shell mathematical model is appropriate, and the problem is solved efficiently using the MITC shell elements, see Refs. [3][4][5][6]. However, if the length scales of the structure are similar in all directions, and the loading is general, then there is no option other than to solve the problem using an assemblage of discrete three-dimensional solid elements, see Refs.…”

Application of DKMQ element for composite plate bending structures

“…Lee and Bathe [20] used the s-norm to evaluate the quadratic MITC plate and MITC shell elements in plate bending problems. Moreover, the application of s-norm for analyzing the shell element has been tested in [21].…”

A direct coupling method for 3D hydroelastic analysis of floating structures

“…If we orthonormalize the rigid body modes with respect to the mass matrix S M and apply Equation (42) into Equation (34), then the part of the structural equation after being multiplied by ‰ T is…”

“…(see, e.g., References [29][30][31][32][33][34][35]). For the fluid boundary element, a four-node quadrilateral element is used, and as for the structural element, the isoparametric interpolation method is adopted for the fluid velocity potential and fluid boundary surface geometry.…”