Bond-slip behavior of CFRP plate-concrete interface

The paper deals with evaluation of the bond performance between a CFRP plate and concrete with respect to various compressive strengths of concrete and bond lengths of the CFRP plate as parameters. To consider stress conditions in the tensile zone of reinforced concrete (RC) structures, double-lap axial tension tests were conducted for eight specimens with CFRP plates bonded to concrete prisms. In addition, a simple linear bond-slip model for the CFRP plate/concrete joints, developed from the bond tests, was used. To verify the model proposed, a total of seven RC beams were strengthened with CFRP plates and tested in flexure employing various bond lengths, strengthening methods, and numbers of CFRP plates. A nonlinear finite-element analysis, with the bond–slip model incorporated in the DIANA program, was performed for the strengthened RC beams. Also, the results of flexural test and analytical predictions are found to be in close agreement in terms of yield and ultimate loads and ductility.     

Static response and free vibration analysis of FGM plates using higher order shear deformation theory

Free vibration and static analysis of functionally graded material (FGM) plates are studied using higher order shear deformation theory with a special modification in the transverse displacement in conjunction with finite element models. 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. The fundamental equations for FGM plates are derived using variational approach by considering traction free boundary conditions on the top and bottom faces of the plate. Results have been obtained by employing a continuous isoparametric Lagrangian finite element with 13 degrees of freedom per node. Convergence tests and comparison studies have been carried out to demonstrate the efficiency of the present model. Numerical results for different thickness ratios, aspect ratios and volume fraction index with different boundary conditions have been presented. It is observed that the natural frequency parameter increases for plate aspect ratio, lower volume fraction index n and smaller thickness ratios. It is also observed that the effect of thickness ratio on the frequency of a plate is independent of the volume fraction index. For a given thickness ratio non-dimensional deflection increases as the volume fraction index increases. It is concluded that the gradient in the material properties plays a vital role in determining the response of the FGM plates.     

Nonlinear finite element analysis of functionally graded plates integrated with patches of piezoelectric fiber reinforced composite

In this paper, a nonlinear static finite element analysis of simply supported smart functionally graded (FG) plates in the presence/absence of the thermal environment has been presented. The substrate FG plate is integrated with the patches of piezoelectric fiber reinforced composite (PFRC) material which act as the distributed actuators of the plate. The material properties of the FG substrate plate are assumed to be temperature dependent and graded along the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The derivation of this nonlinear thermo-electro-mechanical coupled finite element model is based on the first order shear deformation theory and the Von Karman type geometric nonlinearity. The numerical solutions of the nonlinear equations of the finite element model are obtained by employing the direct iteration method. The numerical illustrations suggest the potential use of the distributed actuator made of the PFRC material for active control of nonlinear deformations of smart FG structures. The effects of volume fraction index of the FG material of the substrate plates and the locations of the PFRC patches on the control authority of the patches are investigated. Emphasis has also been placed on investigating the effect of variation of piezoelectric fiber orientation angle in the PFRC patches on their actuation capability for counteracting the large deflections of FG plates.     

C0 FE model based on HOZT for the analysis of laminated soft core skew sandwich plates: Bending and vibration

Bending and free vibration behaviour of laminated soft core skew sandwich plate with stiff laminate face sheets is investigated using a recently developed C₀ finite element (FE) model based on higher order zigzag theory (HOZT) in this paper. The in-plane displacement fields are assumed as a combination of a linear zigzag function with different slopes at each layer and a cubically varying function over the entire thickness. The out of plane displacement is considered to be quadratic within the core and constant in the face sheets. The plate theory ensures a shear stress-free condition at the top and bottom surfaces of the plate. Thus, the plate theory has all of the features required for accurate modelling of laminated skew sandwich plates. As very few element model based on this plate theory (HOZT) exist and they possess certain disadvantages, an attempt has been made to check the applicability of the refined element model. The nodal field variables are chosen in such a manner that there is no need to impose any penalty stiffness in the formulation. Refined C₀ finite element model has been utilized to study some interesting problems on static and free vibration analysis of laminated skew sandwich plates.     

Optimization of the static and dynamic characteristics of plates with isogrid stiffeners

In this paper, the orientation angles of stiffeners arranged in the form of isogrid configuration over a flat plate are selected to optimize the static and dynamic characteristics of these plates/stiffeners assemblies. The static characteristics are optimized by maximizing the critical buckling loads of the isogrid plate, while the dynamic characteristics are optimized by maximizing multiple natural frequencies of the stiffened plate.

A finite element model is developed to describe the statics and dynamics of Mindlin plates which are stiffened with arbitrarily oriented stiffeners. The model is used as a basis for optimizing separately or simultaneously the critical buckling loads and natural frequencies of the plates per unit volume of the plates/stiffeners assemblies.

Numerical examples are presented to demonstrate the utility of the developed model and optimization procedures. The presented approach can be invaluable in the design of plates with isogrid stiffeners for various vibration and noise control applications.     

An analytical solution for bending of transversely isotropic thick rectangular plates with variable thickness

In this study, the bending solution of simply supported transversely isotropic thick rectangular plates with thickness variations is provided using displacement potential functions. To achieve this purpose, governing partial differential equations in terms of displacements are obtained as the quadratic and fourth order. Then, the governing equations are solved using the separation of variables method satisfying exact boundary conditions. The advantage of the purposed method is that there is no limitation on the thickness of the plate or the way the plate thickness is being varied. No simplifying assumption in the analysis process leads to the applicability and reliability of the present method to plates with any arbitrarily chosen thickness. In order to confirm the accuracy of the proposed solution, the obtained results are compared with existing published analytical works for thin variable thickness and thick constant thickness plate. Also, due to the lack of analytical research on thick plates with variable thickness, the obtained results are verified using the finite element method which shows excellent agreement. The results show that the maximum displacement of the plates with variable thickness is moved from the center toward the thinner plate edge. In addition, results exhibit the profound effects of both thickness and aspect ratio on stress distribution along the thickness of the plate. Results also show that varying thickness has not a profound impact on bending and twisting moments in transversely isotropic plates. Five different materials consist of four transversely isotropic and one isotropic, as a special case, are considered in this paper, which it is shown that the material properties have a more considerable impact on higher thickness plate.     

Buckling of laminated plates - A simple finite element based on higher-order theory

A four-noded rectangular element with seven degrees of freedom at each node is developed for buckling analysis of laminated plate structures having any number of layers with a constant thickness of individual layers. The displacement model is so chosen that it can explain adequately the parabolic distribution of transverse shear stresses and the non-linearity of in-plane displacements across the thickness. A geometrical stiffness matrix is developed using in-plane stresses. A wide range of plates from thick to thin are examined under uniaxial loading conditions. The results are compared with the existing analytical and numerical solutions. The present formulations confirm its applicability for buckling analysis of a wide range of plates.     

任意四边形杂交Mindlin板单元

本文把基于虚功原理的杂交有限元模型用于板弯曲问题，构造了一个考虑横向剪应变的任意四边形新型板单元，本单元的突出优点是采用了一种比较合理的位移插值函数，使之能较真实地模拟各类板的变形，且用的自由度最少。文中对此单元作了比较广泛的数值试验，计算结果表明它对板厚有相当宽的适用范围，对于各种例题均能在较粗的网格下得到满意的精度．     

Free vibration analysis of piezoelectric coupled annular plates with variable thickness

This paper presents the free vibration analysis of piezoelectric coupled annular plates with variable thickness on the basis of the Mindlin plate theory. No work has yet been done on piezoelectric laminated plates while the thickness is variable. Two piezoelectric layers are embedded on the upper and lower surfaces of the host plate. The host plate thickness is linearly increased in the radial direction while the piezoelectric layers thicknesses remain constant along the radial direction. Different combinations of three types of boundary conditions i.e. clamped, simply supported, and free end conditions are considered at the inner and outer edges of plate. The Maxwell static electricity equation in piezoelectric layers is satisfied using a quadratic distribution of electric potential along the thickness. The natural frequencies are obtained utilizing a Rayleigh–Ritz energy approach and are validated by comparing with those obtained by finite element analysis. A good compliance is observed between numerical solution and finite element analysis. Convergence study is performed in order to verify the numerical stability of the present method. The effects of different geometrical parameters such as the thickness of piezoelectric layers and the angle of host plate on the natural frequencies of the assembly are investigated.     

Modeling of amplitude-dependent damping characteristics of fiber reinforced composite thin plate

A damping model of fiber reinforced composite thin plate with consideration of amplitude-dependent property is established using the Jones–Nelson nonlinear theory in conjunction with the classical laminated plate theory, polynomial fitting method and strain energy method. In this model, the elastic moduli are expressed as the function of strain energy density and the loss factors in the longitudinal, transverse and shear directions are expressed as the functions of excitation amplitude. Moreover, three TC300 carbon/epoxy composite plates are taken as research objects to carry out a case study. One of them is used to determine the amplitude-dependent coefficients of loss factors in fiber reinforced composites by combining the least square method with polynomial fitting method, and the other two plates are used to verify the correctness of the theoretical model. The results of the developed model considering amplitude dependence and experimental test show a good consistency. It is discovered that the viscoelastic effect of epoxy resin materials will contribute to the increased degree of damping. So, if such plate structures exhibit more pronounced viscoelastic characteristics, there will be more significant in the nonlinear degree of amplitude-dependent damping phenomenon.