Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections

This paper investigates the nonlinear vibration of imperfect shear deformable laminated rectangular plates comprising a homogeneous substrate and two layers of functionally graded materials (FGMs). A theoretical formulation based on Reddy's higher-order shear deformation plate theory is presented in terms of deflection, mid-plane rotations, and the stress function. A semi-analytical method, which makes use of the one-dimensional differential quadrature method, the Galerkin technique, and an iteration process, is used to obtain the vibration frequencies for plates with various boundary conditions. Material properties are assumed to be temperature-dependent. Special attention is given to the effects of sine type imperfection, localized imperfection, and global imperfection on linear and nonlinear vibration behavior. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with graded silicon nitride/stainless steel layers. It is shown that the vibration frequencies are very much dependent on the vibration amplitude and the imperfection mode and its magnitude. While most of the imperfect laminated plates show the well-known hard-spring vibration, those with free edges can display soft-spring vibration behavior at certain imperfection levels. The influences of material composition, temperature-dependence of material properties and side-to-thickness ratio are also discussed. (C) 2004 Elsevier Ltd. All rights reserved.

Non-linear analysis of the thermo-electro-mechanical behaviour of shear deformable FGM plates with piezoelectric actuators

This paper investigates the non-linear bending behaviour of functionally graded plates that are bonded with piezoelectric actuator layers and subjected to transverse loads and a temperature gradient based on Reddy's higher-order shear deformation plate theory. The von Karman-type geometric non-linearity, piezoelectric and thermal effects are included in mathematical formulations. The temperature change is due to a steady-state heat conduction through the plate thickness. The material properties are assumed to be graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The plate is clamped at two opposite edges, while the remaining edges can be free, simply supported or clamped. Differential quadrature approximation in the X-axis is employed to convert the partial differential governing equations and the associated boundary conditions into a set of ordinary differential equations. By choosing the appropriate functions as the displacement and stress functions on each nodal line and then applying the Galerkin procedure, a system of non-linear algebraic equations is obtained, from which the non-linear bending response of the plate is determined through a Picard iteration scheme. Numerical results for zirconia/aluminium rectangular plates are given in dimensionless graphical form. The effects of the applied actuator voltage, the volume fraction exponent, the temperature gradient, as well as the characteristics of the boundary conditions are also studied in detail. Copyright (C) 2004 John Wiley Sons, Ltd.

Hybrid knowledge representation in a blackboard KBS for liquid retaining structure design

This paper highlights the importance of design expertise, for designing liquid retaining structures, including subjective judgments and professional experience. Design of liquid retaining structures has special features different from the others. Being more vulnerable to corrosion problem, they have stringent requirements against serviceability limit state of crack. It is the premise of the study to transferring expert knowledge in a computerized blackboard system. Hybrid knowledge representation schemes, including production rules, object-oriented programming, and procedural methods, are employed to express engineering heuristics and standard design knowledge during the development of the knowledge-based system (KBS) for design of liquid retaining structures. This approach renders it possible to take advantages of the characteristics of each method. The system can provide the user with advice on preliminary design, loading specification, optimized configuration selection and detailed design analysis of liquid retaining structure. It would be beneficial to the field of retaining structure design by focusing on the acquisition and organization of expert knowledge through the development of recent artificial intelligence technology. (C) 2003 Elsevier Ltd. All rights reserved.

An Analytical Solution for the Elastic Lateral-Distortional Buckling of I-section Beams

Lateral-distortional buckling may occur in I-section beams with slender webs and stocky flanges. A computationally efficient method is presented in this paper to study this phenomenon. Previous studies on distortional buckling have been on the use of 3(rd) and 5(th) order polynomials to model the displacements. The present study provides an alternative way, using Fourier Series, to model the behaviour. Beams of different cross-sectional dimensions, load cases and restraint conditions are examined and compared. The accuracy and versatility of the method are verified by calibrating against the results of other published studies. The present method is believed to be a simple and efficient way of determining the buckling load and mode shapes of I-section beams that are susceptible to lateral-distortional buckling modes.

Ultimate strength of continuous composite beams in combined bending and shear

The contributions of the concrete slab and composite action to the vertical shear strength of continuous steel-concrete composite beams are ignored in current design codes, which result in conservative designs. This paper investigates the ultimate strength of continuous composite beams in combined bending and shear by using the finite element analysis method. A three-dimensional finite element model has been developed to account for the geometric and material nonlinear behaviour of continuous composite beams. The finite element model is verified by experimental results and then used to study the effects of the concrete slab and shear connection on the vertical shear strength. The moment-shear interaction strength of continuous composite beams is also investigated by varying the moment/ shear ratio. It is shown that the concrete slab and composite action significantly increase the ultimate strength of continuous composite beams. Based on numerical results, design models are proposed for the vertical shear strength and moment-shear interaction of continuous composite beams. The proposed design models, which incorporates the effects of the concrete slab, composite action, stud pullout failure and web shear buckling, are compared with experimental results with good agreement. (C) 2003 Elsevier Ltd. All rights reserved.

Distortional buckling of I-beams by finite element method

Distortional buckling, unlike the usual lateral-torsional buckling in which the cross-section remains rigid in its own plane, involves distortion of web in the cross-section. This type of buckling typically occurs in beams with slender web and stocky flanges. Most of the published studies assume the web to deform with a cubic shape function. As this assumption may limit the accuracy of the results, a fifth order polynomial is chosen here for the web displacements. The general line-type finite element model used here has two nodes and a maximum of twelve degrees of freedom per node. The model not only can predict the correct coupled mode but also is capable of handling the local buckling of the web.

An expert system on design of liquid-retaining structures with blackboard architecture

The design of liquid-retaining structures involves many decisions to be made by the designer based on rules of thumb, heuristics, judgement, codes of practice and previous experience. Structural design problems are often ill structured and there is a need to develop programming environments that can incorporate engineering judgement along with algorithmic tools. Recent developments in artificial intelligence have made it possible to develop an expert system that can provide expert advice to the user in the selection of design criteria and design parameters. This paper introduces the development of an expert system in the design of liquid-retaining structures using blackboard architecture. An expert system shell, Visual Rule Studio, is employed to facilitate the development of this prototype system. It is a coupled system combining symbolic processing with traditional numerical processing. The expert system developed is based on British Standards Code of Practice BS8007. Explanations are made to assist inexperienced designers or civil engineering students to learn how to design liquid-retaining structures effectively and sustainably in their design practices. The use of this expert system in disseminating heuristic knowledge and experience to practitioners and engineering students is discussed.

Strength analysis of steel-concrete composite beams in combined bending and shear

Despite experimental evidences, the contributions of the concrete slab and composite action to the vertical shear strength of simply supported steel-concrete composite beams are not considered in current design codes, which lead to conservative designs. In this paper, the finite element method is used to investigate the flexural and shear strengths of simply supported composite beams under combined bending and shear. A three-dimensional finite element model has been developed to account for geometric and material nonlinear behavior of composite beams, and verified by experimental results. The verified finite element model is than employed to quantify the contributions of the concrete slab and composite action to the moment and shear capacities of composite beams. The effect of the degree of shear connection on the vertical shear strength of deep composite beams loaded in shear is studied. Design models for vertical shear strength including contributions from the concrete slab and composite action and for the ultimate moment-shear interaction ate proposed for the design of simply supported composite beams in combined bending and shear. The proposed design models provide a consistent and economical design procedure for simply supported composite beams.

Factors affecting the design and construction of Lamella suspen-dome systems

The suspen-dome system is a new structural form that has become popular in the construction of long-span roof structures. These domes are very slender and lightweight, their configuration is complicated, and hence sequential consideration in the structural design is needed. This paper focuses on these considerations, which include the method for designing cable prestress force, a simplified analysis method, and the estimation of buckling capacity. Buckling is one of the most important problems for dome structures. This paper presents the findings of an intensive buckling study of the Lamella suspen-dome system that takes geometric imperfection, asymmetric loading, rise-to-span ratio, and connection rigidity into consideration. Finally, suggested design and construction guidelines are given in the conclusion of this paper. (c) 2005 Elsevier Ltd. All rights reserved.

Evaluation of parameters effective in FRP shear strengthening of RC beams using FE method

Shear strengthening is required when an RC beam is found deficient in shear, or when its shear capacity falls below its flexural capacity after flexural strengthening. A recent technique for the shear strengthening of RC beams is to provide additional FRP web reinforcement, commonly in the form of bonded external FRP strips/sheets. Over the last few years, several experimental studies have been conducted on this new strengthening technique, which has established its effectiveness. While experimental methods of investigation are extremely useful in obtaining information about the composite behaviour of FRP and reinforced concrete, the use of numerical models such as the one presented in this paper helps in developing a good understanding of the behaviour at lower costs. In the study presented in this paper, ANSYS finite element program is used to examine the response of beams strengthened in shear by FRPs. The FE model is calibrated against test results performed at the University of Kentucky. Once validated, the model is used to examine the influence of fibre orientation, compressive strength of concrete, area of tensile and compressive reinforcements, and amount and distance between stirrups on the strength and ductility of FRP strengthened beam.

Influence of imperfect interfaces on bending and vibration of laminated composite shells

This paper is devoted to modeling elastic behavior of laminated composite shells, with special emphasis on incorporating interfacial imperfection. The conditions of imposing traction continuity and displacement jump across each interface are used to model imperfect interfaces. Vanishing transverse shear stresses on two free surfaces of a shell eliminate the need for shear correction factors. A linear theory underlying elastostatics and kinetics of laminated composite shells in a general configuration is presented from Hamilton's principle. In the special case of vanishing interfacial parameters, this theory reduces to the conventional third-order zigzag theory for perfectly bonded laminated shells. Numerical results for bending and vibration problems of laminated circular cylindrical panels are tabulated and plotted to indicate the influence of the interfacial imperfection. (C) 2000 Elsevier Science Ltd. All rights reserved.

Vibration of symmetrically laminated thick super elliptical plates

This paper reports a free vibration analysis of thick plates with rounded corners subject to a free, simply-supported or clamped boundary condition. The plate perimeter is defined by a super elliptic function with a power defining the shape ranging from an ellipse to a rectangle. To incorporate transverse shear deformation, the Reddy third-order plate theory is employed. The energy integrals incorporating shear deformation and rotary inertia are formulated and the p-Ritz procedures are used to derive the governing eigenvalue equation. Numerical examples for plates with different shapes and boundary conditions are solved and their frequency parameters, where possible, are compared with known results. Parametric studies are carried out to show the sensitivities of frequency parameters by varying the geometry, fibre stacking sequence, and boundary condition. (C) 1999 Academic Press.