Journal of Engineering Mechanics

A discrete‐layer, high‐order theory for the stress and displacement analyses of thick, doubly curved laminated shells is presented. The displacements of the shell in the theory are assumed to be layer‐by‐layer high‐order polynomial functions through the shell thickness. The displacement continuity conditions at the interface between layers are imposed as constraints and are introduced into the potential energy functional by Lagrange multipliers. A set of governing equations and the admissible boundary conditions are given on the basis of the theory by applying the generalized variational principle. The analytical solutions of crossply doubly curved shells with shear diaphragm supports are obtained by using the Fourier series expansion method. They are then compared with the 3D elasticity solutions and the analytical solutions obtained from other laminated shell theories. The present theory indicates very close agreement with 3D elasticity solutions.

This paper investigates the effect of foundation rigidity on impedance functions for a circular foundation on a viscoelastic soil medium. In addition to vertical and rocking impedances, the paper also investigates the influence on coupling impedance for horizontal and rocking motions of foundation and horizontal impedance. To generate impedance functions for flexible foundation, a substructure technique is used. For the substructure of the flexible foundation, classical plate theory with neglecting inertial force is employed to obtain the deformation of the foundation due to the interaction stress. For the substructure of the soil medium, the technique, which can deal with wave equations in cylindrical coordinates with arbitrarily prescribed boundary conditions, is employed to obtain the displacement field in the soil medium due to the interaction stresses. Then, with the help of the variational principle, the displacement continuity condition of both substructures is imposed to generate the impedances for the flexible foundation. To demonstrate the effectiveness of the presented procedure, comparison with some previous numerical results is made. Selected numerical results of the presented procedure are presented. Also, comparison between results with and without the assumption of relaxed stress condition is given in order to show the significance of the assumption.

This paper presents a detailed investigation of the shakedown behavior of thick‐walled hollow spheres subjected to cyclic temperature and sustained internal and external pressures. It is found that under sustained and cyclic loadings, the steady states can always be attained for kinematic hardening materials, and the shakedown mode is usually determined by the response during the first cycle. A program is thus developed to determine the mode of the response and the interaction diagram. Then, various steady‐state solutions can be derived following the elastic‐plastic deformation patterns using the general formulation and the incremental method developed in another paper published by Jiang in 1994. Based on a thorough study of the hollow‐sphere behavior, we find that nine different kinds of response are possible. The steady‐state solutions for all these cases are discussed and given in this paper.

The problem of static penetration of an object through a sea ice plate is studied as a two‐dimensional fracture problem using linear elastic fracture mechanics. The ice sheet floating on water is modeled as a thin elastic plate resting on Winkler's elastic foundation. The equilibrium equations are established by minimizing the potential energy approximated by finite differences in terms of nodal deflections. The growth of radial cracks is analyzed using the plate bending theory. The fracture process zone is assumed to be a point in the plane of plate. The maximum load is found to occur when circumferential cracks begin to form, which is governed by a strength criterion. As a refinement and extension of a previous idea, a theory of initial crack spacing is proposed to estimate the number of radial cracks formed during penetration. This theory can also explain the change of the failure mechanism, from failure by formation of circumferential cracks to failure by a conic crack. Particular attention is paid to the size effect. In addition to the size effect described by a simplified one‐dimensional solution in a previous paper, the influence of the difference in the number of radial cracks on the size effect is discovered and analyzed.

A new approach to the analysis of the wave‐induced, hydroelastic response of floating, slender structures is developed that combines a three‐dimensional structural model with fluid forces from two‐dimensional potential theory (strip theory). Because a three‐dimensional finite‐element model of the structure is used, the method allows direct computation of three‐dimensional structural response, such as individual member forces and stresses. However, because a two‐dimensional fluid model is used, the large computational effort of three‐dimensional hydroelasticity (primarily a result of three‐dimensional potential theory) is avoided. The composite 2D/3D method is verified by satisfactory agreement with results from full three‐dimensional hydroelasticity for a SWATH (small water‐plane area twin‐hull) ship. The results indicate that the method may be useful in design of large, slender structures, such as ships, because the computational effort is significantly less than required in 3D hydroelasticity.

The conventional nonlocal model, often used as a localization limiter for continuum‐based constitutive laws with strain‐softening, has been based on an isotropic averaging function. It has recently been shown that this type of nonlocal averaging leads to a model that cannot satisfactorily reproduce experimental results for very different test geometries without modifying the value of the characteristic length depending on geometry. A micromechanically based enrichment of the nonlocal operator by a term taking into account the directional dependence of crack interactions can be expected to improve the performance of the nonlocal model. The aim of this paper is to examine this new model in the context of a simple localization problem reducible to a one‐dimensional description. Strain localization in an infinite layer under plane stress is studied using both the old and the new nonlocal formulations. The importance of a renormalization of the averaging function in the proximity of a boundary is demonstrated and the differences between the localization sensitivity of the old and new model are pointed out. In addition to the detection of bifurcations from an initially uniform state, the stable branch of the load‐displacement diagram is followed using an incremental procedure.

A class of nonlinear oscillator that scales input‐output relations is identified and studied in this paper. This type of system shows variable stiffness, variable damping, or both, and is piecewise linear in conical regions of the state space. The following passive and semiactive mechanical systems, which exhibit this variable structure, are used to motivate the discussion: structures containing energy‐dissipating devices with different loading and unloading stiffnesses, structures with variable dampers, arid structures with active variable stiffness. The free‐vibration response of single‐degree‐of‐freedom systems with variable stiffness and variable damping is computed. It is demonstrated that the period of oscillation and the decay ratio between consecutive peaks of this type of nonlinear system are independent of the amplitude of oscillation. The statistical‐linearization method is used to estimate the mean‐square response of structures containing nonlinear homogeneous devices and subjected to random excitation. Excellent accuracy is achieved in the estimation of the mean‐square response of these oscillators using the statistical‐linearization method.

When subjected to undrained cyclic loading, cohesionless soils are known to build up pore‐water pressure to the extent that the soil loses the effective confining pressure completely, leading to what is known as liquefaction. Presented in this paper is an elastoplastic model that is capable of describing the stress‐strain behavior of sands during such an event. The model is developed by modifying an earlier model, which was shown to be capable of modeling the behavior of sands during monotonic loading. Two procedures, one employing an associated flow rule and another employing a nonassociated flow rule, are proposed for modeling the pore pressure and strain responses during stress reversal, and their potential for modeling liquefaction behavior is explored. The model's capability is examined by comparing the theoretical predictions with experimental triaxial responses.