Development of a Three Dimensional Finite Element for a Composite Layer Consisting of Adhesive Bonding

Modal analysis on full-scale test structures is very expensive and time consuming. Therefore, it is necessary to develop accurate numerical models using the experimental test results to be used for dynamic response analysis or structural modifications. Using precise formulations for representing adhesive layers in composite materials is a key step in constructing the numerical models for compound structures. In a general case of modeling layers, the thickness of the layer and rotation degrees of freedom should be considered for the adhesive element. The recommended element for this case is an eight-node three dimensional element with one translational and two in-plane rotational degrees of freedom per node. These degrees of freedom for adhesive element would be compatible with degrees of freedom of plate elements.It’s not possible to determine shape functions of this kind of element with classical finite element methods, because of excessive unknown factors in polynomials used for describing the displacement field in the element. The proposed solution consists of using a transformation of 20-nodes solid element and its shape functions to an eight-node element. Because of this kind of definition for rotational degree of freedom the model will face with some zero strain modes leading to zero eigenvalues in stiffness matrix. An inverse method named Generic element helps to remove some undesirable properties of the stiffness matrix of this element and make it more consistent with a real model.

Keywords:

Finite Element Method , Adhesive Layer , Zero Strain Modes , Generic Element