Journal of Engineering Mechanics

Using the fully implicit rule for temporal integration, one may define a class of simple plasticity models, for which an incremental potential energy can be constructed. This potential has, in general, multiple stationary points, which correspond to equilibrium solutions when the material shows softening characteristics. Explicit expressions of the incremental potential energy are derived for von Mises plasticity with linear isotropic hardening within the context of a standard dissipative material. Using the Hill criterion for static stability, we show that stable incremental solutions are also (local) minimum points of the incremental potential energy for this particular material. Finite element results for this (simple) plasticity model are presented, which show that the stable solution also exhibits strong localization of plastic deformation.

Random fields are often used in reliability analysis to model the uncertainties that possess spatial variabilities. Within the framework of finite element reliability methods, the domain of each field is discretized into a mesh of random field elements and the value for each element is represented by a single random variable. The selection of random field mesh is important since it influences the accuracy of the reliability analysis. In this study, how to select and refine the random field mesh in finite element reliability analysis is investigated. An expression is derived to compare the improvements made by various refinements of a coarse mesh. Further exploration of the expression shows that the gradient of the limit‐state function plays a key role in the selection of a random field mesh. A criterion for selecting random field meshes is devised as follows: Adopt a coarse mesh in the area where the gradient of the limit‐state function with respect to the discretized variables is small, and a fine mesh in the area where the gradient is large. The selection rule developed in this study is verified by a beam and a plate examples.

The objective of this paper is to develop a simple mechanical model for the analysis and design of plain or fiber‐reinforced concrete shear key joints. The method makes use of well‐known results of fracture mechanics and truss model theory, combined in a simple model. The analysis employs a single discrete crack model under wedging force and a smeared crack model under remote shear force. The proposed formulation identifies two main fracture mechanisms for shear‐off failure of key joints: single curvilinear cracking and development of multiple diagonal cracks. Furthermore, as a first step in developing design aids for the shear strength of shear keys, a simple design formula is obtained. The procedures developed in this study would be useful in designing shear key joints according to the precast concrete segmental method of construction, which is becoming increasingly popular.

The objective of this paper is to verify a mechanical model for the failure of plain or fiber‐reinforced concrete shear key joints through the comparison of the model's prediction with both experimental measurements and finite element method (FEM) analysis results. In the comparison with experimental results, both entire load‐displacement relations and the maximum shear stress or the shear strength of shear keys are considered. The comparison with nonlinear FEM analysis results is also carried out in terms of the load‐displacement relations to supplement the assessment of the mechanical model's validity. The model is found in good agreement with both experiments and FEM analysis, indicating that it can be used as a reliable tool for predicting the response of shear key joints.

The problem of a beam prestessed by means of a stretched cable slipping along a path rigidly linked to the beam is analyzed in a more general and unitary way than in previous formulations by considering nonlinear materials and generic cable paths. Moreover, the writers intend to show that the weak form of the problem, based on total potential energy minimization, is far more convenient than the strong form, based on local equilibrium, from both formal and numerical points of view. The weak form expresses global equilibrium conditions, and describes in a more natural way the physical behavior of this system in which the slipping cable joins the local equilibrium to the global deformation. A numerical method for the solution of the nonlinear problem is provided by using the Ritz approximation method, and results concerning a concrete beam are reported.

In this paper, a model is described that provides a numerical simulation of flow in a contracting cavity with a single outlet and arbitrary user‐supplied wall motion. The numerical solution is obtained by discretizing the Navier‐Stokes equations for viscous fluid flow using the finite analytic (FA) method. This model is first compared with a closed‐form potential flow solution using a spherical geometry. Then the model is applied to flow within the left ventricle of the human heart using successive cine‐angiographic images of the left ventricular outline to obtain wall boundary conditions as input to the model. Qualitative differences existed between the potential and viscous flow solutions, clearly proving the importance of viscous effects and casting doubt on the use of potential flow models in the study of left ventricular fluid dynamics. Simulations of abnormal left ventricular wall movement displayed asymmetric flow, backflow, recirculation, and decreased pressure gradients compared with simulations of normal wall movement.

The most frequently used approach for representing the constitutive relations for anisotropic materials is Hill's incremental plasticity model. However, a fundamental difficulty with the use of Hill's plasticity model is the need to select a unique effective stress‐effective strain relation when none truly exists. Recently, an alternative model based upon stress invariants that does not require definition of an effective stress‐effective strain relation has been proposed. In this study, the invariant‐based model and Hill's model are implemented in a general finite element system. The invariant‐based model is reviewed and a modification is proposed that improves performance for certain multiaxial stress states. Performance of the modified invariant‐based model relative to Hill's model is measured. Comparisons are based upon finite element micromechanics analysis and experimental test results. The invariant‐based model is shown to be superior to Hill's model for a variety of uniaxial and multiaxial loading conditions, but this model is limited to predicting inelastic behavior of transversely isotropic materials.

Stability of a newly proposed structural system, namely the prebuckled (prestressed) sandwich arch is investigated. Stability of prestressed elastica arches with sandwich or homogeneous sections are compared through a parametric study of various geometric and mechanical factors by using a nonlinear finite element model. Results indicate that for prestressed sandwich elastica arches the relative thickness and shear modulus of the core layer not only affect the critical load of the arch, but may also change its governing mode of buckling. On the other hand, flexural rigidity of the core layer does not have a significant impact on the buckling load. Also, the bifurcation loads of prestressed sandwich arches increase almost proportionally with the rise parameter of the arch. The category of prestressed elastica arches can be optimized by using sandwich construction since prestressed sandwich arches are shown to be less vulnerable to loading imperfections leading to sidesway buckling. The effects are more pronounced for sandwich sections with thicker and softer cores.

A two‐step hybrid analytical technique is presented for the nonlinear vibration analysis of thin‐walled beams. The first step involves the generation of various‐order perturbation functions using the Linstedt‐Poincaré perturbation technique. The second step consists of using the perturbation functions as coordinate (or approximation) functions and then computing both the amplitudes of these functions and the nonlinear frequency of vibration via a direct variational procedure. The analytical formulation is based on a form of the geometrically nonlinear beam theory with the effects of in‐plane inertia, rotatory inertia, and transverse shear deformation included. The effectiveness of the proposed technique is demonstrated by means of a numerical example of thin‐walled beam with a doubly symmetric I‐section. The solutions obtained using a single‐spatial mode were compared with those obtained using multiple‐spatial modes. The standard of comparison was taken to be the frequencies obtained by the direct integration/fast Fourier transform (FFT) technique. The nonlinear frequencies obtained by the hybrid technique were shown to converge to the corresponding ones obtained by the direct integration/fast Fourier transform (FFT) technique well beyond the range of applicability of the perturbation technique. The frequencies and total strain energy of the beam were overestimated by using a single‐spatial mode.

The nonlinear free‐surface flow in an infinitely long channel during earthquakes is analyzed by the boundary element method. The solution is obtained by a distribution of simple Rankine‐type singularities on the walls of the channel and on the undisturbed free surface. The fluid in the channel is assumed to be inviscid and incompressible, and its motion irrotational. Unsteady velocity potential is determined with second‐order nonlinear boundary conditions applied on the free surface. The time‐marching procedure is introduced to solve for the transient stage after an earthquake takes place. The channel is assumed to be rigid during an earthquake, and the amplitude of the channel oscillation and the free‐surface elevation are assumed to be small such that the free‐surface boundary conditions are represented by Taylor‐series expansions about the mean water surface. An overview is given for the present approach, and numerical results are presented for two‐dimensional flows due to horizontal, harmonic ground accelerations, including comparisons between linear and nonlinear solutions.

In the framework of three‐dimensional elastostatics and a higher‐order structural mechanics theory, an exact formulation is presented for the torsionless axisymmetric load‐transfer problem of a thin‐walled cylindrical pile of finite length embedded in a semi‐infinite medium. By virtue of a set of integral representations for the responses of the pile and the half‐space under arbitrary interfacial loads, the tangential and radial conditions of contact in the soil‐structure interaction problem are shown to be reducible to a system of Fredholm integral equations. Through an auxiliary analysis, the orders of the singularities of the contact load distributions can be determined mathematically. The results are incorporated into a numerical procedure for the solution of the Fredholm integral equations. Typical solutions for the contact load transfers, the internal axial force variation, and the displacement response as a function of various material and geometric parameters are included to illustrate the fundamental characteristics of the mechanical‐interaction problem.

A method is presented in which the time‐dependent creep response of a three‐filament cord, constrained by a no‐end rotation boundary condition, may be predicted. This method is an initial attempt to describe the viscoelastic response of the cord by incorporating the stress‐relaxation data for a linearly viscoelastic construction material. The particular material used in this paper is polymethyl methacrylate (PMMA). The stress relaxation for PMMA is modeled analytically by utilizing the Schapery collocation method that determines the constant coefficient values for the elements of a Wiechert response model. The geometric effects of the cord are then combined with the time‐dependent analytical solution for the Wiechert model to develop a system of convolution integrals that satisfy the equilibrium and imposed boundary conditions for the cord construction. The solutions for these integrals are approximated numerically using a modified Newton's iterative method combined with a linear time‐step approximation technique.

A new method is presented for the analysis of the buckling strength of imperfection‐sensitive structures. The method can take into account all possible sources of structural imperfections and all the significant imperfection components. It is based on a regular perturbation expansion of the prebuckling response of the structure around the prebuckling response of the corresponding perfect structure. The analysis results in the solution of a generalized eigenvalue problem in terms of a universal imperfection magnitude parameter. The method is illustrated with its application to the analysis of the buckling of a column on a linear elastic foundation. The variability of all the material and the geometric properties of the structure is considered. Numerical results are obtained that reveal certain inadequacies of Koiter's theory in practical applications and the necessity for the new method. They also demonstrate the significant effect of other imperfection sources, besides the shape imperfections, and the significant effect of a multitude of imperfection components, besides those having the shape of the active classical buckling mode.

A procedure is presented for the ultimate‐capacity analysis of space trusses whose members have either buckled or yielded. Unlike previous analyses, which carry out a static analysis to account for member postbuckling behavior, the possibility of a dynamic response due to snap‐through behavior of buckled struts is considered. Whether a dynamic response does occur depends on the stiffness of the degraded space truss vis‐à‐vis the negative member postbuckling stiffness. Studies of a simple truss model and a large double‐layer space truss indicate that neglect of the dynamic response due to member snap‐through leads to a significant overestimate of the structure's capacity.