Showing papers in "Journal of Applied Mechanics in 1982"

Vibration Modes of Centrifugally Stiffened Beams

Abstract: The method of Frobenius is used to solve for the exact frequencies and mode shapes for rotating beams in which both the flexural rigidity and the mass distribution vary linearly. Results are tabulated for a variety of situations including uniform and tapered beams, with root offset and tip mass, and for both hinged root and fixed root boundary conditions. The results obtained for the case of the uniform cantilever beam are compared with other solutions, and the results of a conventional finite-element code.

Stress Analysis for Anisotropic Hardening in Finite-Deformation Plasticity

Abstract: : Kinematic hardening represents the anisotropic component of strain hardening by a shift of the center of the yield surface in stress space. The current approach in stress analysis at finite deformation includes rotational effects by using the Jaumann derivatives of the shift and stress tensors. This procedure generates the unexpected result that oscillatory shear stress is predicated for monotonically increasing simple shear strain. A theory is proposed which calls for a modified Jaumann derivative based on the spin of specific material directions associated with the kinematic hardening. This eliminates the spurious oscillation. General anisotropic hardening is shown to require a similar approach. (Author)

Plasticity Analysis of Laminated Composite Plates

Abstract: Elastic-plastic behavior of symmetric metal-matrix composite laminates is analyzed for the case of in-plane mechanical loading. The overall response of the laminate at each instant is derived from the elastic-plastic deformation of the individual fibrous layers, and from their mutual constraints. Constitutive equations of the laminated plates are presented in terms of initial yield conditions, hardening rules, and instantaneous compliances. Local stresses, hardening parameters, and strains are found in each lamina and in the fiber and matrix phases within each lamina. Specific results are obtained with the continuum model of elastic-plastic fibrous composites [1] which has been recently developed by the authors. Comparisons of analytical results with experimental measurements are made for certain laminated plates.

Application of the line-spring model to a cylindrical shell containing a circumferential or axial part-through crack

Abstract: An approximate solution was obtained for a cylindrical shell containing a part-through surface crack. It was assumed that the shell contains a circumferential or axial semi-elliptic internal or external surface crack and was subjected to a uniform membrane loading or a uniform bending moment away from the crack region. A Reissner type theory was used to account for the effects of the transverse shear deformations. The stress intensity factor at the deepest penetration point of the crack was tabulated for bending and membrane loading by varying three dimensionless length parameters of the problem formed from the shell radius, the shell thickness, the crack length, and the crack depth. The upper bounds of the stress intensity factors are provided by the results of the elasticity solution obtained from the axisymmetric crack problem for the circumferential crack, and that found from the plane strain problem for a circular ring having a radial crack for the axial crack. The line-spring model gives the expected results in comparison with the elasticity solutions. Results also compare well with the existing finite element solution of the pressurized cylinder containing an internal semi-elliptic surface crack.

A Unified, Self-Consistent Theory for the Plastic-Creep Deformation of Metals

Abstract: A unified, self-consistent scheme is formulated to determine the plastic-creep behavior of metals under combined stress. It is pointed out that such a deformation involves the transition from the inhomogeneity to transformation problem in the sense of Eshelby. The plastic deformation is studied by the Berveiller and Zaoui modification of Hill's model. Following plastic deformation the structure of selfconsistent relation for subsequent creep is analyzed and found to be independent of prior plastic strains. These self-consistent relations are used in conjunction with one set of unified constitutive equations for slip systems, in which the effect of prior plastic strains on the subsequent creep is considered. This unified, self-consistent scheme is applied to predict the plastic-creep strains of a 304 stainless steel. As compared to the experimental data, the self-consistent scheme is found to consistently provide reasonably accurate estimates for the total inelastic strains, while the predictions by the von Mises theory are seen to be less favorable.

A Simple and Effective Pipe Elbow Element—Interaction Effects

Abstract: Our elbow element presented in an earlier communication is enhanced to account for interaction effects between elbows and rigid flanges, elbows of different cur­ vatures, and elbows joining straight pipe sections. The interaction effects are modeled by including the appropriate additional strain terms in the stiffness matrix formulation and by using a penalty procedure to enforce the continuity of the derivatives in the pipe skin radial displacements. The enhancement in the formulation has been implemented and the results of various sample analyses are presented.

The steady-state response of a class of dynamical systems to stochastic excitation

Abstract: In this paper a class of coupled nonlinear dynamical systems subjected to stochastic excitation is considered. It is shown how the exact steady-state probability density function for this class of systems can be constructed. The result is then applied to some classical oscillator problems.