Simplified Laminate Theory

This chapter starts with the fundamental description of one-dimensional bar and thin beam members. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law (here: one-dimensional Hooke’s law for isotropic materials), and the equilibrium equation, the partial differential equations, which describe both mechanical members, are derived. In addition to the separate equations for both members, a formal notation is introduced for the combined bar/beam member. The second part of this chapter focuses on composite bar/beam elements with different layers. Based on a generalized stress-strain relationship, the calculation steps based on the simplified classical laminate theory are introduced. The simplifications come from the application of one-dimensional members and the treatment of each single layer as an isotropic material. Based on the internal reactions, i.e., the internal normal force and the internal bending moment, the strain and stress distribution in each single layer can be evaluated. These values may serve then for a subsequent failure analysis based on different criteria.