• Structural Engineering and Mechanics
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• 제88권1호
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• pp.83-94
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• 2023

An accurate and highly efficient inverse element labelled iPCB is developed based on the inverse finite element method (iFEM) for real-time shape estimation of plane-curved structures (such as arch bridges) utilizing onboard strain data. This inverse problem, named shape sensing, is vital for the design of smart structures and structural health monitoring (SHM) procedures. The iPCB formulation is defined based on a least-squares variational principle that employs curved Timoshenko beam theory as its baseline. The accurate strain-displacement relationship considering tension-bending coupling is used to establish theoretical and measured section strains. The displacement fields of the isoparametric element iPCB are interpolated utilizing nonuniform rational B-spline (NURBS) basis functions, enabling exact geometric modelling even with a very coarse mesh density. The present formulation is completely free from membrane and shear locking. Numerical validation examples for different curved structures subjected to different loading conditions have been performed and have demonstrated the excellent prediction capability of iPCBs. The present formulation has also been shown to be practical and robust since relatively accurate predictions can be obtained even omitting the shear deformation contributions and considering polluted strain measures. The current element offers a promising tool for real-time shape estimation of plane-curved structures.

• Steel and Composite Structures
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• 재36권6호
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• pp.643-656
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• 2020

This article presents a comprehensive static analysis of simply supported cross-ply carbon nanotubes reinforced composite (CNTRC) laminated nanobeams under various loading profiles. The nonlocal strain gradient constitutive relation is exploited to present the size-dependence of nano-scale. New higher shear deformation beam theory with hyperbolic function is proposed to satisfy the zero-shear effect at boundaries and parabolic variation through the thickness. Carbon nanotubes (CNTs), as the reinforced elements, are distributed through the beam thickness with different distribution functions, which are, uniform distribution (UD-CNTRC), V- distribution (FG-V CNTRC), O- distribution (FG-O CNTRC) and X- distribution (FG-X CNTRC). The equilibrium equations are derived, and Fourier series function are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear or sinusoidal mechanical loadings. Numerical results are obtained to present influences of CNTs reinforcement patterns, composite laminate structure, nonlocal parameter, length scale parameter, geometric parameters on center deflection ad stresses of CNTRC laminated nanobeams. The proposed model is effective in analysis and design of composite structure ranging from macro-scale to nano-scale.

• Smart Structures and Systems
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• 제16권5호
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• pp.781-806
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• 2015

A unified formulation of finite layer methods (FLMs), based on the Reissner mixed variational theorem (RMVT), is developed for the three-dimensional (3D) coupled electro-elastic analysis of simply-supported, functionally graded piezoelectric material (FGPM) plates with open- and closed-circuit surface conditions and under electro-mechanical loads. In this formulation, the material properties of the plate are assumed to obey an exponent-law varying exponentially through the thickness coordinate, and the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the primary field variables of each individual layer, respectively, such as the elastic displacement, transverse shear and normal stress, electric potential, and normal electric displacement components. The relevant orders used for expanding these variables in the thickness coordinate can be freely chosen as the linear, quadratic and cubic orders. Four different mechanical/electrical loading conditions applied on the top and bottom surfaces of the plate are considered, and the corresponding coupled electro-elastic analysis of the loaded FGPM plates is undertaken. The accuracy and convergence rate of the RMVT-based FLMs are assessed by comparing their solutions with the exact 3D piezoelectricity ones available in the literature.

• Wind and Structures
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• 제8권5호
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• pp.357-372
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• 2005

Mean and extreme pressure distributions on a large cantilevered flat roof model are measured in a boundary layer wind tunnel. The largest peak suction values are observed from pressure taps beneath conical "delta-wing type" corner vortices that occur for oblique winds, then the characteristics and causes of the local peak suctions are discussed in detail. Power spectra of fluctuating wind pressures measured from some typical taps located at the roof edges under different wind directions are presented, and coherence functions of fluctuating pressures are also obtained. Based on these results, it is verified that the peak suctions are highly correlated with the conical vortices. Furthermore, according to the characteristics of wind loads on the roof, an aerodynamic solution to minimize the peak suctions by venting the leading edges and the corners of the roof is recommended. The experimental results show that the suggested strategy can effectively control the generation of the conical vortices and make a reduction of 50% in mean pressures and 25% in extreme local pressures at wind sensitive locations on the roof.

• Wind and Structures
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• 제18권1호
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• pp.1-20
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• 2014

Modern design of long suspension bridges must satisfy at the same time spanning very long distances and limiting their response against several external loads, even if of high intensity. Structural Control, with the solutions it provides, can offer a reliable contribution to limit internal forces and deformations in structural elements when extreme events occur. This positive aspect is very interesting when the dimensions of the structure are large. Herein, an updated numerical model of an existing suspension bridge is developed in a commercial finite element work frame, starting from original data. This model is used to reevaluate an optimization procedure for a passive control strategy, already proven effective with a simplified model of the buffeting wind forces. Such optimization procedure, previously implemented with a quasi-steady model of the buffeting excitation, is here reevaluated adopting a more refined version of the wind-structure interaction forces in which wind actions are applied on the towers and the cables considering drag forces only. For the deck a more refined formulation, based on the use of indicial functions, is adopted to reflect coupling with the bridge orientation and motion. It is shown that there is no variation of the previously identified optimal passive configuration.

• Structural Engineering and Mechanics
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• 제29권5호
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• pp.469-488
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• 2008

Finite element methods have often been used for structural analyses of various mechanical problems. When finite element analyses are utilized to resolve mechanical systems, numerical uncertainties in the initial data such as structural parameters and loading conditions may result in uncertainties in the structural responses. Therefore the initial data have to be as accurate as possible in order to obtain reliable structural analysis results. The typical finite element method may not properly represent discrete systems when using uncertain data, since all input data of material properties and applied loads are defined by nominal values. An interval finite element analysis, which uses the interval arithmetic as introduced by Moore (1966) is proposed as a non-stochastic method in this study and serves a new numerical tool for evaluating the uncertainties of the initial data in structural analyses. According to this method, the element stiffness matrix includes interval terms of the lower and upper bounds of the structural parameters, and interval change functions are devised. Numerical uncertainties in the initial data are described as a tolerance error and tree graphs of uncertain data are constructed by numerical uncertainty combinations of each parameter. The structural responses calculated by all uncertainty cases can be easily estimated so that structural safety can be included in the design. Numerical applications of truss and frame structures demonstrate the efficiency of the present method with respect to numerical analyses of structural uncertainties.

• Steel and Composite Structures
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• 제34권1호
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• pp.75-89
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• 2020

The current paper illustrates the effect of in-plane varying compressive force on critical buckling loads and buckling modes of sandwich composite laminated beam rested on elastic foundation. To generalize a proposed model, unified higher order shear deformation beam theories are exploited through analysis; those satisfy the parabolic variation of shear across the thickness. Therefore, there is no need for shear correction factor. Winkler and Pasternak elastic foundations are presented to consider the effect of any elastic medium surrounding beam structure. The Hamilton's principle is proposed to derive the equilibrium equations of unified sandwich composite laminated beams. Differential quadrature numerical method (DQNM) is used to discretize the differential equilibrium equations in spatial direction. After that, eigenvalue problem is solved to obtain the buckling loads and associated mode shapes. The proposed model is validated with previous published works and good matching is observed. The numerical results are carried out to show effects of axial load functions, lamination thicknesses, orthotropy and elastic foundation constants on the buckling loads and mode shapes of sandwich composite beam. This model is important in designing of aircrafts and ships when non-uniform compressive load and shear loading is dominated.

• Structural Engineering and Mechanics
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• 제76권3호
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• pp.325-336
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• 2020

In this study, the continuous and discontinuous contact problems of functionally graded (FG) layer resting on a rigid foundation were considered. The top of the FG layer was loaded by a distributed load. It was assumed that the shear modulus and the density of the layer varied according to exponential functions along the depth whereas the the Poisson ratio remained constant. The problem first was solved analytically and the results were verified with the ones obtained from finite element (FE) solution. In analytical solution, the stress and displacement components for FG layer were obtained by the help of Fourier integral transform. Critical load expression and integral equation for continuous and discontinuous contact, respectively, using corresponding boundary conditions in each case. The finite element solution of the problem was carried out using ANSYS software program. In continuous contact case, initial separation distance and contact stresses along the contact surface between the FG layer and the rigid foundation were examined. Separation distances and contact stresses were obtained in case of discontinuous contact. The effect of material properties and loading were investigated using both analytical and FE solutions. It was shown that obtained results were compatible with each other.

• Structural Engineering and Mechanics
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• 제53권4호
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• pp.703-723
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• 2015

In this paper optimization of volume fraction distribution in a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) and subjected to steady state thermal and mechanical loadings is considered. The finite element method with graded material properties within each element (graded finite elements) is used to model the structure. Volume fractions of constituent materials on a finite number of design points are taken as design variables and the volume fractions at any arbitrary point in the cylinder are obtained via cubic spline interpolation functions. The objective function selected as having the normalized effective stress equal to one at all points that leads to a uniform stress distribution in the structure. Genetic Algorithm jointed with interior penalty-function method for implementing constraints is effectively employed to find the global solution of the optimization problem. Obtained results indicates that by using the uniform distribution of normalized effective stress as objective function, considerably more efficient usage of materials can be achieved compared with the power law volume fraction distribution. Also considering uniform distribution of safety factor as design criteria instead of minimizing peak effective stress affects remarkably the optimum volume fractions.

• 한국자동차공학회논문집
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• 제15권2호
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• pp.101-108
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• 2007

This paper presents an efficient meshless method for analyzing cracked piezoelectric structures subjected to mechanical and electrical loading. The method employs an element free Galerkin (EFG) formulation and an enriched basic function as well as special shape functions that contain discontinuous derivatives. Based on the moving least squares (MLS) interpolation approach, The EFG method is one of the promising methods for dealing with problems involving progressive crack growth. Since the method is meshless and no element connectivity data are needed, the burdensome remeshing procedure required in the conventional finite element method (FEM) is avoided. The numerical results show that the proposed method yields an accurate near-tip stress field in an infinite piezoelectric plate containing an interior hole. Another example is to study a ceramic multilayer actuator. The proposed model was found to be accurate in the simulation of stress and electric field concentrations due to the abrupt end of an internal electrode.