In this paper, a higher-order theory is derived for laminates consisting of isotropic layers, on the basis of three-dimensional elasticity with displacements as higher-order functions of z in the thickness direction. The theory employs three stress potentials, Ψ (an Airy function), p (a harmonic function), and its conjugate q, to satisfy all conditions of stress equilibrium and compatibility. Interlaminar shear stresses, i.e., antiplane stresses, are shown to be present at the interfaces, especially near material discontinuities where gradients of in-plane stresses are usually high. For illustrating its practical application, the problem of a plate containing a hole patched with an intact plate is solved.
A test method for the determination of the shear modulus and the modulus of elasticity of laminated anisotropic composite materials is presented. Two tests are required. In one test, a ring is simply supported at two diametrically opposite supports and subjected to two diametrically opposite concentrated loads normal to the plane of the ring and located 90° from the supports. The second test employs a split ring. Each end of the ring is subjected to a concentrated load normal to the plane of the ring. By conducting these two tests and measuring the normal deflections corresponding to the applied loads, shear modulus and modulus of elasticity of the ring can be determined from the formulas derived in the paper. It should be noted that for laminated composite anisotropic materials these moduli cannot be determined from the tests as known in the literature, one of which involves out-of-plane loading and the other an in-plane loading as suggested in Paper 4709, Douglas Missile and Space Systems Division, McDonnell Douglas Corporation, November, 1967.
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