Journal of Engineering Mechanics

It has long been recognized that the strength of a thin, axially compressed, unstiffened cylinder is governed by bifurcation into a nonsymmetric displacement mode, that the strength is acutely sensitive to very small geometric imperfections of the surface, and that internal pressure increases the strength markedly. In many practical applications, axially compressed cylinders are simultaneously subject to internal pressure, so the problem is a common one. Despite many theoretical and experimental studies, the strength gains due to internal pressure cannot yet be defined with confidence, and a match between laboratory testing, field imperfection measurement, theoretical bifurcation prediction, and allowable design strength has not yet been achieved. The conservatism of current designs is thus still in doubt. This paper addresses the problem of elastic unstiffened thin cylinders with axisymmetric imperfections, as some field measurements indicate that these imperfections are common in civil engineering structures, and since they are known to be very detrimental to buckling strengths. The paper investigates the effects of sinusoidal, local inward, and local outward imperfections. It tries to explain why Hutchinson's classic theory of 1965 for pressurized imperfect elastic cylinders predicts much lower strengths than those predicted for cylinders with more practical imperfection forms.

Dynamic vibration absorbers with one degree of freedom are generally applied to the passive control of beam vibration. These absorbers are useful to control a single mode of vibration under harmonic excitation. In this paper, a beam‐type dynamic vibration absorber is presented and is composed of a beam (dynamic absorbing beam) under the same boundary conditions as the main beam and uniformly distributed, connecting spring and damper between the main beam and absorbing beam. Equations of motion of the system in modal coordinates of the main beam become equal to those of the two‐degrees‐of‐freedom system with two masses and three springs. Formulas for optimum design of the beam‐type dynamic vibration absorber are proposed by using the optimum design method of a dynamic absorber in two degrees of freedom, obtained by Den Hartog's method. Numerical calculations indicated the response of the main beam without damping is reduced with the exception of the response of the second mode, and the one with damping is remarkably reduced.

A uniaxial constitutive model for ice is developed in which the total strain is taken to be the sum of instantaneous elastic, delayed elastic, and viscous strain components. Nonlinear behavior of selected terms in the model allow the representation of softening due to internal damage. The predictions of the uniaxial model are compared with published test results for constant strain‐rate, constant stress, and constant stress‐rate tests. The model is generalized for plane stress, and predictions are compared with published data for biaxial tests.

The objective of this paper is to present the complete force‐displacement relationship for a Timoshenko beam element resting on a two‐parameter elastic foundation. Both the stiffness matrix and nodal‐action column‐vector coefficients are derived from the transport matrix based on the exact solution of two differential equations governing the problem concerned herein. Explicit expressions for the element stiffness matrix and the nodal‐action column vectors are presented. Finally, a parametric study is carried out in the form of numerical examples and influence lines.

High‐strength welded steel cruciforms are tested under variable‐amplitude loadings to determine the effect of the root‐mean‐square (rms) of the loading process on the rate of fatigue‐damage accumulation. All variable‐amplitude loadings are narrow‐band and have Rayleigh distributed extrema. The only loading parameter that is varied from one set of experiments to the next is the rms value. Constant‐amplitude tests also are performed to determine the S‐N curve for these cruciforms. Using the constant‐amplitude test results and the Rayleigh approximation method, variable‐amplitude fatigue‐life predictions also are obtained. Comparison of experimental results with analytical predictions indicate that for loadings with relatively high rms values (compared with the specimen's yield strength), the analytical predictions are about twice as long as the experimental fatigue lives. For loadings with intermediate rms values, the analytical predictions generally are in good agreement with experimental results. For loadings with low rms values, the analytical predictions can be twice as long as the experimental results, depending on the interpretation of constant‐amplitude test results in the high‐cycle region.

A 40‐degree‐of‐freedom displacement‐type rectangular finite element for shear deformable flat plates is presented. The element includes transverse shear effects, is fully conforming, may be orthotropic, and has a stiffness that may be obtained by closed‐form integration. The element does not appear to lock. Numerical examples for plates with uniform loads and for simply supported and clamped boundary conditions are presented and compared with results from other investigators. These results demonstrate that this element is more flexible than most other finite elements for moderately thick plates. The results also agree well with those from a numerical solution of the three‐dimensional elasticity equations. Convergence to thin‐plate theory is obtained when the length‐to‐thickness ratio is large or when the transverse shear moduli are artificially increased.

Polynomial interpolation functions for finite element analysis of three‐dimensional (3‐D) curved beams are derived using small deformation theory. The performance of low‐order polynomials combined with selectively reduced integration is evaluated under torsional and membrane “locking” conditions. Low‐order polynomials are also used in a three‐field mixed formulation; in this approach, the constraint equations of the problems that result from the nonlinear geometry of the curved beam are enforced using collocation. It is shown that the proposed technique eliminates “locking” from the formulation. The resulting interpolation functions are coupled in pairs, reflecting the dependence that occurs between in‐plane flexural translation and axial deformation, and between out‐of‐plane flexural translation and torsional rotation in beams that are curved in plan. Consistent element stiffness and mass matrices obtained using the proposed functions represent properties of slender curved beams, and converge to those of a 3‐D straight‐frame element when the geometric curvature of the member becomes infinitely small.

A study is made of the thermomechanical buckling of composite plates subjected to combined thermal and axial loadings. The plates considered consist of a number of perfectly bonded layers and have symmetric lamination with respect to the middle plane. The material properties are assumed to be independent of temperature. The analysis is based on a first‐order shear deformation theory. A mixed formulation is used, with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. An efficient multiple‐parameter reduction method is used, in conjunction with mixed finite‐element models, for determining the stability boundary of the plate. Sensitivity derivatives are evaluated and used to study the sensitivity of the buckling response to variations in different lamination and material parameters of the plate. Numerical results are presented that show the effectiveness of the reduction method, as well as the effects of variations in the material characteristics and fiber orientation of individual layers on the stability boundary of the plate.

A system of finite dimensional rigid bodies, such as a masonry arch, can be interpreted as a nonholonomic system in which there are constraints on the generalized coordinates. The potential energy function for a system of rigid blocks can be written as a mathematical programming problem: Minimize the potential energy subject to kinematic constraints on the degrees of freedom. A solution to this problem is a stable equilibrium state. Well‐known results from the theory of optimization are applied to the solution. This formulation of the problem leads to a useful interpretation of the Lagrangian multipliers, from which the lower‐bound condition of plastic analysis is directly obtained as a sufficient condition for the stability of the system. The upper‐bound condition, which is also recovered from this formulation of the problem, is not a sufficient condition for instability of all systems. However, it is shown that for most systems of practical significance, the upper‐bound condition is a sufficient condition for instability, and the lower‐bound condition is a necessary condition for stability.

The theoretical relationships between eigenfrequency changes and magnitudes and the locations of crack‐induced damage are developed for beam structures with either simply supported or cantilever boundary conditions. For uniform beams, a physical model of a massless rotational spring is used to represent the local flexibility introduced by the crack. A characteristic equation is derived as a base for the development of the relationship. A symbolic computational package, MACSYMA, is used to facilitate the computations of the higher‐order determinant and the corresponding derivatives involved in the characteristic equations. For nonuniform beams, the concept of receptance is used for a system linked with two coordinates (axial and rotational coordinates). Numerical experiments involving the use of a finite‐element program, SAP, to determine the eigenfrequencies of both uniform and nonuniform beams with a variety of damage scenarios are used to validate the derived theoretical relationships. The comparisons between the predicted and simulated damage conditions are satisfactory. Two important assumptions are involved in the derived relationship: one is that the structure is considered to behave linearly, and the other one is that the elastic properties of the structure member are time‐invariant. The application of the theoretical model is discussed at the end of the paper.

Two‐dimensional particles experience shear bands as real granular materials; they form a convenient vehicle to investigate shear bands within granular soils. Numerical simulations on these idealized materials are used to assess the assumptions and limitations of the shear‐band analyses that are based on linear stability theory and micropolar continua. These shear‐band analyses are found to be applicable in the postbifurcation range, and they describe the thickness of shear bands and the displacements and rotations of the particles within the shear bands of idealized granular materials. The influence of particle rotation within shear bands validates the use of micropolar models. The thickness of shear bands is strongly influenced by the model parameters controlling the micropolar effects. The constitutive models based on the deformation and flow theories of plasticity predict similarly the emergence and inclination of shear bands, but give different shear‐band thicknesses.

Using a mixed‐mode extension of the Hillerborg fictitious crack model, a practical interface finite element approach is used to model discrete crack propagation. The fictitious crack tip propagates perpendicular to the maximum tensile principal stress at its tip when the tensile strength is exceeded. A dynamic relaxation method is employed. Interface elements have been used before to model such cracks; however, the software technology is in a state of rapid development, making possible improvements in the modeling of discrete nonlinear crack propagation. The concept of fracture process zone is broadened to one of interface process zone, which includes the nonlinear behavior of the fracture process zone as well as the crack face interference behind the fracture process zone. A development makes the method efficient while preserving the accuracy of the fictitious crack model. The fictitious crack is represented by interface elements with linearly varying displacements; however, the traction distribution is arbitrary. As example problems demonstrate, these assumptions allow the fictitious crack to be modeled using few degrees of freedom without compromising accuracy. Modeling of the size effect is presented.