• Structural Engineering and Mechanics
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• v.8 no.6
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• pp.607-622
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• 1999

Being a significant mode of deformation, shear effect in addition to the other modes of stretching and bending have been considered to develop two finite element models for the analysis of beams on elastic foundation. The first beam model is developed utilizing the differential-equation approach; in which the complex variables obtained from the solution of the differential equations are used as interpolation functions for the displacement field in this beam element. A single element is sufficient to exactly represent a continuous part of a beam on Winkler foundation for cases involving end-loadings, thus providing a benchmark solution to validate the other model developed. The second beam model is developed utilizing the hybrid-mixed formulation, i.e., Hellinger-Reissner variational principle; in which both displacement and stress fields for the beam as well as the foundation are approxmated separately in order to eliminate the well-known phenomenon of shear locking, as well as the newly-identified problem of "foundation-locking" that can arise in cases involving foundations with extreme rigidities. This latter model is versatile and indented for utilization in general applications; i.e., for thin-thick beams, general loadings, and a wide variation of the underlying foundation rigidity with respect to beam stiffness. A set of numerical examples are given to demonstrate and assess the performance of the developed beam models in practical applications involving shear deformation effect.

• Structural Engineering and Mechanics
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• v.19 no.5
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• pp.477-501
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• 2005

In this study, a new smart beam finite element is proposed for the finite element modeling of beam-type smart structures that are equipped with bonded plate-type piezoelectric sensors and actuators. Constitutive equations for the direct piezoelectric effect and converse piezoelectric effect of piezoelectric materials are considered in the formulation. By using a variational principle, the equations of motion for the smart beam finite element are derived. The proposed 2-node beam finite element is an isoparametric element based on Timoshenko beam theory. The proposed smart beam finite element is applied to the free vibration control adopting a constant gain feedback scheme. The electrical force vector, which is obtained in deriving an equation of motion, is the control force equivalent to that in existing literature. Validity of the proposed element is shown through comparing the analytical results of the verification examples with those of other previous researchers. With the use of smart beam finite elements, simulation of free vibration control is demonstrated by sensing the voltage of the piezoelectric sensors and by applying the voltages to the piezoelectric actuators.

• Steel and Composite Structures
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• v.31 no.6
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• pp.591-600
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• 2019

Based on the energy-variational principle, a coupling vibration analysis model of high-speed railway simply supported beam bridge-track structure system (HSRBTS) was established by considering the effect of shear deformation. The vibration differential equation and natural boundary conditions of HSRBTS were derived by considering the interlayer slip effect. Then, an analytic calculation method for the natural vibration frequency of this system was obtained. By taking two simply supported beam bridges of high-speed railway of 24 m and 32 m in span as examples, ANSYS and MIDAS finite-element numerical calculation methods were compared with the analytic method established in this paper. The calculation results show that two of them agree well with each other, validating the analytic method reported in this paper. The analytic method established in this study was used to evaluate the natural vibration characteristics of HSRBTS under different interlayer stiffness and length of rails at different subgrade sections. The results show that the vertical interlayer compressive stiffness had a great influence on the high-order natural vibration frequency of HSRBTS, and the effect of longitudinal interlayer slip stiffness on the natural vibration frequency of HSRBTS could be ignored. Under different vertical interlayer stiffness conditions, the subgrade section of HSRBTS has a critical rail length, and the critical length of rail at subgrade section decreases with the increase in vertical interlayer compressive stiffness.

• Steel and Composite Structures
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• v.43 no.5
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• pp.533-552
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• 2022

The current article deals with the dynamic stability, and structural improvement of vibrating electrically curved screen on the viscoelastic substrate. By considering optimum value for radius curvature of the electrically curved screen, the structure improvement of the system occurs. For modeling the electrically system, the Maxwell's' equation is developed. Hertz contact model in employed to obtain contact forces between impactor and structure. Moreover, variational methods and nonlinear von Kármán model are used to derive boundary conditions (BCs) and nonlinear governing equations of the vibrating electrically curved screen. Galerkin and Multiple scales solution approach are coupled to solve the nonlinear set of governing equations of the vibrating electrically curved screen. Along with the analytical solution, 3D finite element simulation via ABAQUS package is provided with the aid of a FE package for simulating the current system's response. The results are categorized in 3 different sections. First, effects of geometrical and material parameters on the vibrational performance and stability of the curves panel. Second, physical properties of the impactor are taken in to account and their effect on the absorbed energy and velocity profile of the impactor are presented. Finally, effect of the radius and initial velocity on the mode shapes of the current structure is demonstrated.

• Structural Engineering and Mechanics
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• v.81 no.6
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• pp.769-780
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• 2022

This paper studies the dynamic behavior of laminated composite circular cylindrical shells interacting with a fluid. The mathematical formulation of the dynamic problem for an elastic body is developed based on the variational principle of virtual displacements and the relations of linear elasticity theory. The behavior of an ideal compressible fluid is described by the potential theory, the equations of which together with boundary conditions are transformed to a weak form. The hydrodynamic pressure exerted by the fluid on the internal surface of the shell is calculated according to the linearized Bernoulli equation. The numerical implementation of the mathematical formulation has been done using the semi-analytical finite element method. The influence of the ply angle and lay-up configurations of laminated composites on the natural vibration frequencies and the hydroelastic stability boundary have been analyzed for shells with different geometrical dimensions and under different kinematic boundary conditions set at their edges. It has been found that the optimal value of the ply angle depends on the level of filling of the shell with a fluid. The obtained results support the view that by choosing the optimal configuration of the layered composite material it is possible to change upwards or downwards the frequency and mode shape, as well as the critical velocity for stability loss over a wide range.

• Advances in nano research
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• v.12 no.2
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• pp.117-137
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• 2022

Effect of thickness stretching on free vibration, bending and buckling behavior of carbon nanotubes reinforced composite (CNTRC) laminated nanoplates rested on new variable elastic foundation is investigated in this paper using a developed four-unknown quasi-3D higher-order shear deformation theory (HSDT). The key feature of this theoretical formulation is that, in addition to considering the thickness stretching effect, the number of unknowns of the displacement field is reduced to four, and which is more than five in the other models. Two new forms of CNTs reinforcement distribution are proposed and analyzed based on cosine functions. By considering the higher-order nonlocal strain gradient theory, microstructure and length scale influences are included. Variational method is developed to derive the governing equation and Galerkin method is employed to derive an analytical solution of governing equilibrium equations. Two-dimensional variable Winkler elastic foundation is suggested in this study for the first time. A parametric study is executed to determine the impact of the reinforcement patterns, nonlocal parameter, length scale parameter, side-t-thickness ratio and aspect ratio, elastic foundation and various boundary conditions on bending, buckling and free vibration responses of the CNTRC plate.

• Structural Engineering and Mechanics
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• v.86 no.1
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• pp.49-68
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• 2023

This study investigates the static and dynamic structural analysis of symmetrical and asymmetrical coupled shear walls using the continuous and modified transfer matrix methods by idealizing the coupled shear wall as a three-field CTB-type replacement beam. The coupled shear wall is modeled as a continuous structure consisting of the parallel coupling of a Timoshenko beam in tension (with axial extensibility in the shear walls) and a shear beam (replacing the beam coupling effect between the shear walls). The variational method using the Hamilton principle is used to obtain the coupled differential equations and the boundary conditions associated with the model. Using the continuous method, closed-form analytical solutions to the differential equation for the coupled shear wall with uniform properties along the height are derived and a numerical solution using the modified transfer matrix is proposed to overcome the difficulty of coupled shear walls with non-uniform properties along height. The computational advantage of the modified transfer matrix method compared to the classical method is shown. The results of the numerical examples and the parametric analysis show that the proposed analytical and numerical model and method is accurate, reliable and involves reduced processing time for generalized static and dynamic structural analysis of coupled shear walls at a preliminary stage and can used as a verification method in the final stage of the project.

• Advances in nano research
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• v.14 no.2
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• pp.141-154
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• 2023

Effects of viscoelastic foundation on vibration of curved-beam structure with clamped and simply-supported boundary conditions is investigated in this study. In doing so, a micro-scale laminate composite beam with two piezoelectric face layer with a carbon nanotube reinforces composite core is considered. The whole beam structure is laid on a viscoelastic substrate which normally occurred in actual conditions. Due to small scale of the structure non-classical elasticity theory provided more accurate results. Therefore, nonlocal strain gradient theory is employed here to capture both nano-scale effects on carbon nanotubes and microscale effects because of overall scale of the structure. Equivalent homogenous properties of the composite core is obtained using Halpin-Tsai equation. The equations of motion is derived considering energy terms of the beam and variational principle in minimizing total energy. The boundary condition is assumed to be clamped at one end and simply supported at the other end. Due to nonlinear terms in the equations of motion, semi-analytical method of general differential quadrature method is engaged to solve the equations. In addition, due to complexity in developing and solving equations of motion of arches, an artificial neural network is design and implemented to capture effects of different parameters on the inplane vibration of sandwich arches. At the end, effects of several parameters including nonlocal and gradient parameters, geometrical aspect ratios and substrate constants of the structure on the natural frequency and amplitude is derived. It is observed that increasing nonlocal and gradient parameters have contradictory effects of the amplitude and frequency of vibration of the laminate beam.

• Advances in nano research
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• v.16 no.3
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• pp.251-263
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• 2024

This article investigates the free vibration behavior of carbon nanotube reinforced composite (CNTRC) beams embedded using variational analytical methods and artificial neural networks (ANN). The material properties of layered functionally graded CNTRC (FG-CNTRC) beams are estimated using nonlocal parameters modified power-law with different types of CNT distributions through the thickness direction of the beam. Adopting Eringen's nonlocal elasticity theory to capture the small size effects, the nonlocal governing equations are derived and solved using the analytical method. And also, the problem was analyzed using the ANN method. The architecture of the proposed ANN model is 3-9-1. In the experiments, we used 112 different data to predict the natural frequency using ANN. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion as well as the boundary conditions of the beam are derived using Hamilton's principle. The classical beam theory is used to formulate a governing equation for predicting the free vibration of laminated CNTRC beams. According to the experimental results, the prediction ability of the ANN model is very good and the natural frequency can be predicted in ANN without attempting any experiments.

• Structural Engineering and Mechanics
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• v.91 no.4
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• pp.383-391
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• 2024

Conical shell is a common engineering structure, which is widely used in machinery, civil and construction fields. Most of them are usually exposed to external environments, temperature is an important factor affecting its performance. If the external temperature is too high, the deformation of the conical shell will occur, leading to a decrease in stability. Therefore, studying the thermal-post buckling behavior of conical shells is of great significance. This article takes graphene platelets reinforced metal foams (GPLRMF) conical shells as the research object, and uses high-order shear deformation theory (HSDT) to study the thermal post-buckling behaviors. Based on general variational principle, the governing equation of a GPLRMF conical shell is deduced, and discretized and solved by Galerkin method to obtain the critical buckling temperature and thermal post-buckling response of conical shells under various influencing factors. Finally, the effects of cone angles, GPLs distribution types, GPLs mass fraction, porosity distribution types and porosity coefficient on the thermal post-buckling behaviors of conical shells are analyzed in detail. The results show that the cone angle has a significant impact on the nonlinear thermal stability of the conical shells.