An analysis of interlaminar shear stresses is performed for a lami nate under generalized plane stresses. The laminate is modeled as a set of anisotropic layers separated by isotropic adhesive layers. The corresponding equilibrium differential equations are developed and solved for laminates of infinite and finite width. In the first case, it is shown that the interlaminar shear stress is zero everywhere, while in the latter case, this stress attains finite maximum values at the edges of the strip. These results are important when interpreting strength data obtained from uniaxial tests.

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Analytical and experimental investigations have been performed in a study of longitudinal inertia effects upon the parametric response of a column under an axial load P(t) = P0 + P1 cos γt. The analysis has led to stability criteria, imposed on the load and longitudinal inertia parameters, which have shown good agreement with experimental results. A certain degree of scatter between experimental runs has been observed, though agreement within (italics) each run has been very good. The scatter, attributed to small misalignments and departure from axiality of loading, stems from the realignment procedure necessary between each experimental run. To facilitate prediction of parametric response, the analytical stability criteria have been plotted in the form of two bounding surfaces of an instability region in a three-dimensional parameter space. Use of this region permits description of the conditions and responses associated with parametric instability, and allows evaluation of the effects of disturbances.

This paper investigates the dynamic response of completely clamped, shallow, thin elastic spherical shells under sustained, uniformly distributed, time-dependent loads of the form P(t) = PO + jPi(t), where the dynamic component Pi(t) is periodic in time t and the average load PO is constant. The investigation is conducted both analytically and experimentally, with particular attention devoted to a) the axisymmetrical responses, b) the critical dynamic load condition, c) the application and extension of the solution techniques, and d) the existence of harmonic responses. Beginning with the Marguerre equations of motion and assuming negligible in-plane inertia loads, a Dini and Fourier-Bessel approach and the principle of harmonic balance lead to the stable, steady-state responses. The experimental work shows that a two-term Bessel solution is excellent for describing dynamic responses for geometry parameters X < 5.6, and is applicable with limitations in the range 5.6 < X < 8.5. Under zero static pressure, the first natural frequencies are satisfactorily predicted for all geometries (A < 14.67) tested. There is good evidence that increasing the number of solution terms will extend the geometry and pressure ranges of applicability. Poor agreement in some cases between the theoretical and experimental results for X > 5.6 suggests strongly that asymmetrical modes of vibration become predominant. The steady-state response of the spherical shell is found to be similar, in many respects, to the response of a soft nonlinear spring under periodic load. The analytically determined "jump" conditions have been found equivalent, in most instances considered, to experimentally observed snap-through conditions. Interaction between dynamic and static load responses precludes the use of superposition in describing the shell response. The dynamic critical load conditions obtained here reduce to the static critical loads when the critical dynamic component tends to zero. NomenclatureOperators, symbols Geometry and material a h R E V D X x t, T base radius uniform thickness radius of curvature cylindrical coordinates of midsurface points Young's modulus Poisson's ratio plate modulus, D = Eh z /12(l -*/ 2 ) geometry parameter X 4 = [12(1 -2 )a 4 ]/ = dimensionless radius, x = r/a = time, dimensionless time Load and response = distributed load = static load, dynamic load = midsurface displacement components = stress function, satisfying in-plane equilibrium = dimensionless transverse displacement, stress function = Eulerian critical pressure, complete sphere = dimensionless distributed pressure = displacement components = load components = excitation frequency, dimensionless frequency, yt = (3r Po, Pi(0