ABSTRACT of the Doctoral Thesis

Semi-Analytical Finite Element Formulations for Layered Shells with Consideration of Edge Effects

by Michael A. Stiftinger (1996)

A semi-analytical approach for predicting the tri-axial stress states near free edges in laminated fiber composites is presented in this work. An analytical solution procedure for the interlaminar stresses which is based on an explicit description of the edge stresses and a minimum energy approach are implemented into a finite shell element formulation. Hence, the interlaminar stresses arising near free edges in layered materials can be calculated within a finite element analysis, using the stress results of the finite element solution as input values for the analytical solution procedure.

For this purpose a new locking-free four noded shell element for laminated fiber reinforced materials is developed. Based on an analytical approach from the literature, which is extended to capture arbitrary stacking sequences and load configurations (including thermal loading), an algorithm for predicting the free edge stress field is derived.

A very general introduction into the field of laminated fiber reinforced materials is given in the beginning of this work. The literature review on the macromechanical treatment of laminated fiber composites focuses on shell theories for laminates, free edge effects, interlaminar stresses, and delamination.

Next, a four noded geometrically nonlinear finite shell element, called the LFC-ANS element (which stands for Laminated Fiber Reinforced Composite - Assumed Natural Strain element), is developed. The derivation of the tangent element stiffness for the Total Lagrangean formulation by degeneration of the three-dimensional stress and strain conditions is presented in detail. A thermo-elastic material description for layered orthotropic materials is employed and the stiffness terms are integrated analytically over the element thickness. To overcome shear locking, the well known approach of modifying the transverse shear strains, proposed by Dvorkin and Bathe, is used, and the element is implemented into the finite element research code CARINA.

A simple nonlinear material description for considering stiffness degradation in a laminate due to ply failure within the context of finite element analyses is presented. The capabilities of this approach are demonstrated in an example which is discussed in detail.

The development of interlaminar stresses near free edges in layered materials is explained clearly. The analytical approach for calculating the interlaminar stresses near free edges presented by Kassapoglou and Lagace for symmetric laminates under uniaxial loading, is extended to make this method applicable to unsymmetric laminates as well, and to allow for combined thermal and mechanical loading, the latter being not restricted to be uniaxial. The solution for the stress state along free edges is found by choosing appropriate trial functions for the stress components that satisfy global as well as local equilibrium conditions, traction continuity across layer boundaries, the stress free boundary conditions at the free edge and at the top and bottom surfaces as well, and that are able to recover the far field stress state calculated by the finite element model. The two unknown parameters in the assumed stress shapes are determined by minimizing the total potential energy of the boundary layer of the laminate.

Numerous results on interlaminar stresses are discussed next. Comparisons with solutions obtained by three-dimensional finite element calculations show good agreement for most of the investigated configurations. Additional results for transversally loaded laminates and for a plate subjected to combined thermal and mechanical loading are presented.

Finally, the semi-analytical approach is summarized and its advantages and shortcomings are discussed.

revised 960522 (hjb)