Date of Completion


Embargo Period



Functionally graded material, Grade finite elements, Quadrilateral elements, Incompatible elements, Isotropically graded, Orthotropically graded, Dynamic analysis, Corrugated core, Sandwich beams, Russell error

Major Advisor

Dr. Jeongho Kim

Associate Advisor

Dr. Ramesh Malla

Associate Advisor

Dr. Wei Zhang

Field of Study

Civil Engineering


Doctor of Philosophy

Open Access

Open Access


Functionally graded materials (FGMs) are non-homogenous and tailored to have a spatial variation of properties. The gradual modification of material properties is quite effective in reducing stresses. Finite element analysis of nonhomogeneous materials can be performed using an assemblage of either graded or homogeneous elements. A graded finite element samples the material property at more than one integration points, while a homogeneous element has constant property at all integration points based on the property of the element at the centroid. In this dissertation, a six-node incompatible graded finite element is developed.

This research aims to show significance of six-node incompatible (QM6) element over four-node compatible (Q4) graded elements in terms of accuracy of the results and computation time. The numerical solution is obtained using UMAT capability of the ABAQUS software. The results are compared with the exact solution (e.g. stress due to far field tension loads for graded infinite plates). Incompatible graded element is shown to give better performance in terms of accuracy over Q4 element and computationally efficient than an eight-node compatible (Q8) element in two-dimensional plane elasticity. Thus six-node incompatible (QM6) is recommended for modelling FGMs.

Furthermore, the dynamic loading characteristics of the shock tube onto sandwich steel beams as an efficient and accurate alternative to time-consuming and complicated fluid-structure interaction using finite element modeling is introduced. Improved accuracy of 3D dynamic analysis using eight-node incompatible brick elements (C3D8I) is demonstrated through this dynamic analysis example and results are compared to lower-order compatible brick elements (C3D8).