Journal of Engineering Mechanics

The field transfer matrix technique is used to investigate the static and dynamic behavior of stiffened linked shear walls. In the determination of the natural frequencies of vibration, the effects of bending, shear and rotatory inertias are included in the analysis. The optimal positions of the stiffening beam are determined to give maximum lateral stiffness, and hence the highest fundamental natural frequency, and minimum tensile stress in the concrete. It is shown that there is an analogy between the behavior of stiffened linked shear walls and outrigger‐braced structures, and the same governing equations apply in each case. The optimal positions for a stiffening beam or an outrigger are identical for the same structural parameters.

A five‐parameter constitutive equation for Ottawa sand at one void ratio is proposed. After an expression for the strain energy function in terms of the stretch ratios is obtained, the various constants in the constitutive relations are determined using experimental test data. The predictive capability of this constitutive model, which is obtained by using the theory of finite deformations, is demonstrated through application to different deformation fields.

Though thin plates have a useful reserve of elastic postbuckling strength, the linear buckling load remains an important design parameter. White and Cottingham have published useful graphs of buckling coefficients versus aspect ratio for various partial edge loadings and for simply‐supported as well as for fixed‐edge boundaries. Some of their graphs exhibit large cusps which they attribute to a change of buckling mode. The writers have written a fairly general finite‐difference plate buckling program in preparation for postbuckling studies; to test the program they recalculated the White and Cottingham results. These recalculations not only removed all cusplike buckling coefficient response for fixed‐edge boundaries but, for one loading case, found that the White and Cottingham coefficients appear 100% too high whereas for another loading case the writers' results were 1/8 higher; for simply‐supported boundaries the results agree closely. The writers' conjecture is that the cusplike behavior found by White and Cottingham is due to erroneous generalized eigenvalue solutions in the previous calculations, removed by the writers' use of reliable EISPACK subroutines.

This paper is concerned with the geometrically nonlinear axisymmetric static and transient analysis of moderately thick cylindrically orthotropic circular plates subjected to uniformly distributed and discrete central loads. Shear deformation and rotary inertia are included in the analysis. Differential equations in terms of the transverse displacement, w, the rotation of the normal to the middle surface, ϕ, and the stress function, ψ, are employed. These three field variables are expanded in finite power series and the discretized equations are obtained by using the orthogonal point collocation method in the space domain and the Newmark‐β scheme in the time domain. Results are presented for immovable clamped and simply supported plates for static and step function loads. The effect of transverse shear is investigated for isotropic, transversely isotropic and orthotropic plates.

The finite element method is used to solve contact problems. The approach is general and is used to solve contact problems between flexible bodies. A system of constitutive relations which are applicable to elasto‐plastic materials subjected to finite strains is used to obtain the deformations and stresses for the contact problems. The materials exhibit both kinematic and isotropic strain‐hardening. An incremental iterative procedure is used to solve this problem. The solution to the Hertz contact problem is presented to demonstrate the applicability of the proposed method.

A method for the analysis of discrete elastoplastic structural systems with proportional damping and subjected to dynamic loads is presented. Firstly, it is shown that, using the mode superposition method, the actual node displacements and generalized stresses can be given suitable integral representations in terms of the known load history and of the unknown plastic strain history; secondly, considering the evolution of the system in a small time step and imposing the relevant laws of (holonomic) plasticity theory at the step extreme times only, it is shown that the step plastic strain increments can be obtained by solving algebraic problems shaped either in the form of a linear complementarity problem, or in the forms of two alternative quadratic programming problems. The formats of these problems are recursive and thus sequentially applicable, such as to cover the entire loading process, in much the same way quasistatic elastoplastic problems can be solved. The resulting numerical procedure turns out to be unconditionally stable, while the only error sources are due to the modeling of the unknown plastic strain history. Imposed strain‐like loads (e.g., thermal shocks) can be considered. A simple numerical example is also presented and a preliminary comparison of the proposed method with other known methods is discussed.

Blast loads on structures are conveniently represented by means of Heaviside step functions. Due to the non‐differentiability of these functions the analytical handling (integration by parts) fails quickly. This problem can be successfully overcome by applying the theory of generalized functions. Calculations for rectangular plates are presented for illustration.

Response of an aging linear system exposed from a certain age $t_0$ to ergodic random input is analyzed. It is shown that the response, while non‐stationary with respect to time and age, is stationary and ergodic with regard to the birth time τ (the time when the system was built). Consequently, the instantaneous statistical characteristics of all possible response realizations at a chosen age, t, may be determined as the characteristics of the response at age t (and at a fixed exposure age, $t_0$) as the birth time τ is varied, i.e., as the input history is shifted in time against the instant when the system was built. Based on this new idea, the spectral method is generalized for aging systems, using a frequency response function and a spectral density of response that depend on both the current age t and the age $t_0$ when the exposure begins. The relation between the spectral densities of input and response is algebraic, similar to the case of stationary response of nonaging systems. For the special case of non‐stationary response of nonaging systems, the proposed new method is simpler than the existing methods. The new method can be applied, e.g., to shrinkage stresses in an aging linearly viscoelastic structure (a concrete structure) exposed to relative humidity fluctuations of weather. A simple illustrative example is solved in a closed form. Another possible application is earthquake motion of a structure undergoing progressive damage, provided the problem is approximated as linear.

Statistical tests on the cohesional and frictional components of shear strength of soils have repeatedly identified these parameters to be more adequately modeled by the beta distribution than by any of the other common two parameter distributions. The beta distribution is theoretically derived as the natural probability law governing the variations of c and tanϕ. The development is based completely on physical understanding on the particulate nature of soils.