• Structural Engineering and Mechanics
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• 제9권3호
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• pp.269-288
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• 2000

The governing differential equations for free vibration of multi-step orthotropic shear plates with variably distributed mass, stiffness and viscous damping are established. It is shown that a shear plate can be divided into two independent shear bars to determine the natural frequencies and mode shapes of the plate. The jk-th natural frequency of a shear plate is equal to the square root of the square sum of the j-th natural frequency of a shear bar and the k-th natural frequency of another shear bar. The jk-th mode shape of the shear plate is the product of the j-th mode shape of a shear bar and the k-th mode shape of another shear bar. The general solutions of the governing equations of the orthotropic shear plates with various boundary conditions are derived by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass along the height of the plates. A numerical example demonstrates that the present methods are easy to implement and efficient. It is also shown through the numerical example that the selected expressions are suitable for describing the distributions of stiffness and mass of typical multi-storey buildings.

• Geomechanics and Engineering
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• 제8권3호
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• pp.305-321
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• 2015

In this paper, a new hyperbolic shear deformation plate theory based on neutral surface position is developed for the static analysis of functionally graded plates (FGPs). The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Based on the present new hyperbolic shear deformation plate theory and the neutral surface concept, the governing equations of equilibrium are derived from the principle of virtual displacements. Numerical illustrations concern flexural behavior of FG plates with Metal-Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, volume fraction profiles, aspect ratios and length to thickness ratios. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Steel and Composite Structures
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• 제26권3호
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• pp.361-373
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• 2018

This paper presents the development of finite element (FE) models to simulate the behavior of diagonally stiffened steel plate shear wall systems (SPSWs) with differently shaped openings subjected to a cyclic load. This walling system has the potential to be used for shear elements that resist lateral loads in steel-framed buildings. A number of $\text\tiny{^1/_2}$-scale one-story buildings that were un-stiffened, stiffened and stiffened with opening SPSWs are modeled and simulated using the finite element method based on experimental data from previous research. After validating the finite element (FE) models, the effects of infill plate thickness on the cyclic behavior of steel shear walls are investigated. Furthermore, triple diagonal stiffeners are added to the steel infill plates of the SPSWs, and the effects are studied. Moreover, the effects of a number of differently shaped openings applied to the infill plate are studied. The results indicate that the bearing capacity and shear resistance are affected positively by increasing the infill plate thickness and by adding triple diagonal stiffeners. In addition, the cyclic behavior of SPSWs is improved, even with an opening in the SPSWs.

• Wind and Structures
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• 제19권4호
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• pp.405-420
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• 2014

This paper examines the nonlinear behaviour of corrugated steel plate shear walls under lateral pushover load. One of the innovations in these types of walls which have used in recent years is the use of the corrugated steel shear walls rather un-stiffness plates. In the last decades many experimental studies have been done on the on the corrugated steel shear walls. A finite element analysis that includes both material and geometric nonlinearities is employed for the investigation. A comparison is made between the behaviour of steel shear walls with sinusoidal corrugated plate and trapezoidal corrugated plate. The effects of parameters such as the thickness of the corrugated plate, the corrugation depth in the corrugated plates and the corrugation length of the infill of the corrugated plates, are investigated. The results of this study have demonstrated that in the wall with constant dimensions, the trapezoidal plates have higher energy dissipation, ductility and ultimate bearing than sinusoidal waves, while decreasing the steel material consumption.

• Earthquakes and Structures
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• 제20권4호
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• pp.377-388
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• 2021

Thin perforated Steel Plate Shear Walls (SPSWs) are among the most common types of seismic energy dissipation systems to protect the main boundary components of SPSWs from fatal fractures in the high-risk zones. In this paper, the cyclic behavior of the different circular hole patterns under cyclic loading is reported. Based on the experimental results, it can be concluded that a change in the perforation pattern of the circular holes leads to a change in the locations of the fracture tendency over the web plate, especially at the plate-frame interactions. Accordingly, the cyclic responses of the tested specimens were simulated by finite element method using the ABAQUS package. Likewise, perforated shear panels with a new perforation pattern obtained by implementing Topology Optimization (TO) were proposed. It was found that the ultimate shear strength of the specimen with the proposed TO perforation pattern was higher than that of the other specimens. In addition, theoretical equations using the Plate-Frame Interaction (PFI) method were used to predict the shear strength and initial stiffness of the considered specimens. The theoretical results showed that the proposed reduced coefficients relationships cannot accurately predict the shear strength and initial stiffness of the considered perforated shear panels. Therefore, the reduced coefficients should be adopted in the theoretical equations based on the obtained experimental and numerical results. Finally, with the results of this study, the shear strength and initial stiffness of these types of perforated shear panels can be predicted by PFI method.

• Structural Engineering and Mechanics
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• 제18권1호
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• pp.79-90
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• 2004

A high precision shear deformable triangular element has been proposed for bending analysis of triangular plate. The element has twelve nodes at the three sides and four nodes inside the element. Initially the element has thirty-five degrees of freedom, which has been reduced to thirty by eliminating the degrees of freedom of the internal nodes through static condensation. Plates having different boundary conditions, side ratios (b/a) and thickness ratios (h/a = 0.001, 0.1 and 0.2) have been analyzed using the proposed shear locking free element. Concentrated and uniformly distributed transverse loads have been used for the analysis. The formulation is made based on first order shear deformation theory. For validation of the present element and formulation few results of thin triangular plate have been compared with the analytical solutions. Results for thick plate have been presented as new results.

• Steel and Composite Structures
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• 제6권1호
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• pp.1-14
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• 2006

Experiments have been carried out on six composite and two plain steel plate girders under shear loading to understand the elastic and inelastic behaviour of such girders. The failure mechanism assumed and used to develop design equations is normally based on the failure patterns observed in the experiments. Therefore, different types of cracks and failure patterns observed in the experiments are reviewed briefly first. Based on the observed failure patterns, a design method to predict the ultimate shear capacity of composite plate girders is proposed in this paper. The values of ultimate shear capacity obtained using the proposed design method are compared with the corresponding experimental values and it is found that the proposed method is able to predict the shear capacity accurately.

• Structural Engineering and Mechanics
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• 제57권6호
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• pp.1107-1124
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• 2016

Consistent finite strain Plate constitutive relations are derived based on a hyperelastic formulation for an isotropic material. Plate equilibrium equations under finite strain are derived following a static kinematic approach. Three Euler angles and four shear angles, based on Timoshenko beam theory, represent the kinematics of the deformations in the plate cross section. The Green deformation tensor has been expressed in term of a deformation tensor associated with the deformation and stretches of an embedded plate element. Buckling formulation includes the in-plane axial deformation prior to buckling and transverse as well as in-plane shear deformations. Numerical results for a simply supported thick plate under uni-axial compression force are presented.

• Structural Engineering and Mechanics
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• 제60권4호
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• pp.547-565
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• 2016

In this work a new 3-unknown non-polynomial shear deformation theory for the buckling and vibration analyses of functionally graded material (FGM) sandwich plates is presented. The present theory accounts for non-linear in plane displacement and constant transverse displacement through the plate thickness, complies with plate surface boundary conditions, and in this manner a shear correction factor is not required. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modelled with only 3 unknowns as the case of the classical plate theory (CPT) and which is even less than the first order shear deformation theory (FSDT). The plate properties are assumed to vary according to a power law distribution of the volume fraction of the constituents. Equations of motion are derived from the Hamilton's principle. Analytical solutions of natural frequency and critical buckling load for functionally graded sandwich plates are obtained using the Navier solution. The results obtained for plate with various thickness ratios using the present non-polynomial plate theory are not only substantially more accurate than those obtained using the classical plate theory, but are almost comparable to those obtained using higher order theories with more number of unknown functions.

• Structural Engineering and Mechanics
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• 제74권3호
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• pp.325-339
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• 2020

This study presents a practical application of topology optimization (TO) technique to seek the best form of perforated steel plate shear walls (PSPSW) in simple frames. For the numerical investigation, a finite element model is proposed based on the recent particular form of PSPSW that is called the ring-shaped steel plate shear wall. The TO is applied based on the sensitivity analysis to maximize the reaction forces as the objective function considering the fracture tendency. For this purpose, TO is conducted under a monotonic and cyclic loading considering the nonlinear behavior (material and geometry) and buckling. Also, the effect of plate thickness is studied on the TO results. The final material volume of the optimized plate is limited to the material volume of the ring-shaped plate. Finally, an optimized plate is introduced and its nonlinear behavior is investigated under a cyclic and monotonic loading. For a more comprehensive view, the results are compared to the ring-shaped and four usual forms of SPSWs. The material volume of the plate for all the models is the same. The results indicate the strength, load-carrying, and energy dissipation in the optimized plate are increased while the fracture tendency is reduced without changing the material volume.