Journal of Engineering Mechanics

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December 1984

Volume 110, Issue 12, pp. 1655-1785

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Improved Technique for Estimating Buckling Loads

Charles W. Bert

J. Eng. Mech. 110, 1655 (1984); http://dx.doi.org/10.1061/(ASCE)0733-9399(1984)110:12(1655) (11 pages) | Cited 3 times

Online Publication Date: 24 December 2008

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An improved version of the Rayleigh technique is applied to prediction of critical buckling loads of prismatic columns, stepped columns, and tapered columns. Both the Rayleigh (curvature) or potential energy expression and the Timoshenko (deflection) or complementary energy are utilized and applied to predicting upper bounds. Results are compared with exact solutions, where available, and with results of other approximate techniques. It is demonstrated that the technique considerably increases the accuracy of both the Rayleigh (one‐term) and Rayleigh‐Ritz (two‐term) techniques, especially when used in conjunction with complementary energy, without requiring the use of more than a hand‐held calculator.

Continuum Theory for Strain‐Softening

Zdeněk P. Bažant, F. ASCE, Ted B. Belytschko, M. ASCE, and Ta‐Peng Chang, S. M. ASCE

J. Eng. Mech. 110, 1666 (1984); http://dx.doi.org/10.1061/(ASCE)0733-9399(1984)110:12(1666) (27 pages) | Cited 12 times

Online Publication Date: 24 December 2008

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In heterogeneous materials such as concretes or rocks, failure occurs by progressive distributed damage during which the material exhibits strain‐softening, i.e., a gradual decline of stress at increasing strain. It is shown that strain‐softening which is stable within finite‐size regions and leads to a nonzero energy dissipation by failure can be achieved by a new type of nonlocal continuum called the imbricate continuum. Its theory is based on the hypothesis that the stress depends on the change of distance between two points lying a finite distance apart. This continuum is a limit of a discrete system of imbricated (regularly overlapping) elements which have a fixed length, l, and a cross‐section area that tends to zero as the discretization is refined. The principal difference from the existing nonlocal continuum theory is that the equation of motion involves not only the averaging of strains but also the averaging of stress gradients. This assures that the finite element stiffness matrices are symmetric, while those obtained for the existing nonlocal continuum theory are not. Broad‐range stresses are distinguished from local stresses and a different stress‐strain relation is used for each—the broad range one with strain‐softening, the local one without it. Stability of the material is analyzed, and an explicit time‐step algorithm is presented. Finally, convergence and stability are numerically demonstrated by analyzing wave propagation in a one‐dimensional bar.

Imbricate Continuum and its Variational Derivation

Zdeněk P. Bažant, F. ASCE

J. Eng. Mech. 110, 1693 (1984); http://dx.doi.org/10.1061/(ASCE)0733-9399(1984)110:12(1693) (20 pages) | Cited 6 times

Online Publication Date: 24 December 2008

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The one‐dimensional imbricate nonlocal continuum, developed in a previous paper in order to model strain‐softening within zones of finite size, is extended here to two or three dimensions. The continuum represents a limit of a system of imbricated (overlapping) elements that have a fixed size and a diminishing cross section as the mesh is refined. The proper variational method for the imbricate continuum is developed, and the continuum equations of motion are derived from the principle of virtual work. They are of difference‐differential type and involve not only strain averaging but also stress gradient averaging for the so‐called broad‐range stresses characterizing the forces within the representative volume of heterogeneous material. The gradient averaging may be defined by a difference operator, or an averaging integral, or by least‐square fitting of a homogeneous strain field. A differential approximation with higher order displacement derivatives is also shown. The theory implies a boundary layer which requires special treatment. The blunt crack band model, previously used in finite element analysis of progressive fracturing, is extended by the present theory into the range of mesh sizes much smaller than the characteristic width of the crack band front. Thus, the crack band model is made part of a convergent discretization scheme. The nonlocal continuum aspects are captured by an imbricated arrangement of finite elements of the usual type.

Continuum Models for Dynamics of Buildings

Sudhir K. Jain

J. Eng. Mech. 110, 1713 (1984); http://dx.doi.org/10.1061/(ASCE)0733-9399(1984)110:12(1713) (18 pages)

Online Publication Date: 24 December 2008

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An analytical method was developed for the dynamic analysis of multistory buildings with significant in‐plane floor flexibility. Expressions are given for the dynamic properties of multistory buildings with end walls (or frames) in the transverse direction. The floors of these structures are idealized as equivalent, distributed beams while the walls or frames are treated as bending or shear beams. The equations of motion and the boundary conditions of the resulting elements are solved exactly to obtain a transcendental characteristic equation that can be solved numerically to obtain natural frequencies. The substitution of these frequencies in the given expressions provides mode shapes and participation factors. The approach was also applied to the analysis of a multistory building with end walls in the upper stories and several walls in the ground story. The Imperial County Services Building, which has a similar system, has been studied using the developed solutions. The method predicts several important features of the complex dynamic behavior of this building.

Extremes of Wave Forces

Mircea Grigoriu, M. ASCE

J. Eng. Mech. 110, 1731 (1984); http://dx.doi.org/10.1061/(ASCE)0733-9399(1984)110:12(1731) (12 pages) | Cited 1 time

Online Publication Date: 24 December 2008

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Probabilistic descriptors are developed for Morison‐type wave forces. They are based on the actual distribution of these forces and on the hypothesis that wave forces follow Gaussian distributions. The Gaussian hypothesis is characteristic of analyses based on statistical linearization. Results show that this hypothesis provides unsatisfactory estimates for the peak of wave forces during design storms. Both the mean and the variance of the peak wave force can be underestimated significantly when the Gaussian hypothesis is applied. It is assumed in the analysis that the wave particle velocity process follows a Gaussian distribution.

Recursive Covariance of Structural Responses

Masaru Hoshiya, Kiyoshi Ishii, and Shigeru Nagata

J. Eng. Mech. 110, 1743 (1984); http://dx.doi.org/10.1061/(ASCE)0733-9399(1984)110:12(1743) (13 pages) | Cited 2 times

Online Publication Date: 24 December 2008

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This paper describes an effective method of obtaining covariance responses in recursive form for a multi‐degree‐of‐freedom linear structural system subjected to nonstationary random excitations. The earthquake excitations are expressed as a multiply‐correlated nonstationary autoregressive process model. By utilizing white noise characteristics of the AR model, this covariance response matrix equation is derived from state space matrix equation with mixed excitations and response components. Then, a torsional vibration model, subjected to two horizontal components of earthquake excitation, is analyzed. A BWR type nuclear power plant building is used as an example to show how recursive covariances are applied to evaluate statistical values of nonstationary maximum responses.

Structural Identification by Extended Kalman Filter

Masaru Hoshiya and Etsuro Saito

J. Eng. Mech. 110, 1757 (1984); http://dx.doi.org/10.1061/(ASCE)0733-9399(1984)110:12(1757) (14 pages) | Cited 11 times

Online Publication Date: 24 December 2008

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The extended Kalman filter is applied to system identification problems of seismic structural systems. In order to obtain the stable and convergent solutions, a weighted global iteration procedure with an objective function is proposed for stable estimation, being incorporated into the extended Kalman filter algorithm. For the effectiveness of this present proposal, the identification problems are investigated for multiple degree‐of‐freedom linear systems, bilinear hysteretic systems, and equivalent linearization of bilinear hysteretic systems. As numerically shown in these examples, the weighted global iteration procedure may be useful to identification problems.
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Mechanical Nonlinear Shear Wall Model

Tarun R. Naik, M. ASCE, Sandor Kaliszky, M. ASCE, and Lawrence A. Soltis, M. ASCE

J. Eng. Mech. 110, 1773 (1984); http://dx.doi.org/10.1061/(ASCE)0733-9399(1984)110:12(1773) (6 pages) | Cited 1 time

Online Publication Date: 24 December 2008

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The nonlinear performance of a shear wall building can often only be described by full-scale testing or nonlinear analysis. Full-scale tests are time consuming and expensive; nonlinear analysis often is mathematically complex so that limiting assumptions are necessary to simplify the problem. This study describes a mechanical model which can simulate the nonlinear static or dynamic response of a shear wall or diaphragm. An assembly of these models can then simulate entire buildings and is suitable for the experimental investigation of the linear and nonlinear, static or dynamic response of shear wall structures.

The Dual of Foulkes and Prager‐Shield Criteria

George I. N. Rozvany, F. ASCE

J. Eng. Mech. 110, 1778 (1984); http://dx.doi.org/10.1061/(ASCE)0733-9399(1984)110:12(1778) (8 pages)

Online Publication Date: 24 December 2008

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After reviewing existing duality principles for structures with continuously variable cross-section (i.e. structures without segmentation), optimality criteria and duality principles are presented for structures with segment-wise constant cross-section. It is shown that the optimal solution for the latter is associated with a displacement field in which the average strain value for each segment is proportional to the subgradient of the specific cost function with respect to the maximum generalized stress value over that segment. Moreover, the dual problem consists of maximizing the difference of two terms. The first of these is the integral of the product of loads and displacements and the second is the sum of the products of segment sizes (length or area) and the mean ``complementary cost.'' The above principles are illustrated with examples and the optimal solutions are verified by independent methods. It is shown that for special cases the proposed optimality criteria reduce to those by Prager-Shield, Masur and Foulkes.
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