The use of modified couple stress theory to simulate the size-dependent phenomenon of composite laminate microplate is commonly limited to simple boundary conditions and mechanical bending load. The ...small-scale effects on bending and buckling on composite laminate microplate under complex boundary conditions in thermal environment have not been understood fully in the literature. Hence, this research develops, for the first time, a model to overcome the above limitation through the combination of a new modified couple stress theory and isogeometric analysis (IGA). By solving the governing equation using IGA, the thermal displacement, stress and thermal buckling load for various material length scale parameters are obtained. To satisfy the continuous shear stress condition at the layer interfaces, the equilibrium equations as integrated in-plane stress derivatives over the thickness are imposed. In addition, the non-uniform rational B-splines (NURBS) satisfy the higher-order derivative of shape function using the equilibrium equation. Furthermore, to show the effectiveness of presented model for capturing the size effect on thermal bending and thermal buckling of multi-ply laminate microplate, the influences of fiber orientation, thickness ratio, boundary condition and the variation in material length scale parameter are investigated.
This paper presents a novel and effective formulation based on isogeometric approach (IGA) and higher-order deformation plate theory (HSDT) to study the behavior of functionally graded material (FGM) ...plates. HSDT model using C1 continuous element is able to improve the accuracy of solution and describe exactly the shear stress distribution without shear correction factors. IGA utilizes the non-uniform rational B-spline (NURBS) functions which allow us to achieve easily the smoothness with arbitrary continuity order. The present method hence fulfills the C1 – requirement of HSDT model. The effective material properties of the FGM plates, which property varies only through the thickness of plate, are calculated using the rule of mixture and the Mori–Tanaka homogenization technique. The static, dynamic and buckling analysis of rectangular and circular plates is investigated for different boundary conditions. Numerical results show high effectiveness of the present formulation.
This paper presents a nonlinear numerical model, which is based on the modified couple stress theory (MCST), and trigonometric shear deformation theory coupled with isogeometric analysis. The present ...approach captures the small scale effects on the geometrically nonlinear behaviors of functionally graded carbon nanotube reinforced composite (FG-CNTRC) micro-plate with four patterns distribution. The equations of motion are established based on a Galerkin weak form associated with von-Kármán nonlinear strains. The MCST utilizes only one material length scale parameter to predict the size effect in FG-CNTRC micro-plate, for which its material properties are derived from an extended rule of mixture. The solutions of nonlinear static equation are obtained by using the Newton–Raphson technique and the Newmark time iteration procedure in association with Picard method is assigned to get responses of the nonlinear dynamic problems. In addition, the Rayleigh damping is applied to consider the influence of damping characteristic on the oscillation of FG-CNTRC micro-plates. Comparisons are performed to verify the proposed approach. Afterward, the numerical examples are used to show the effects of the distribution of carbon nanotubes (CNT), their volume fraction, the material length scale parameter and the boundary conditions on the nonlinear static and dynamic behaviors of FG-CNTRC micro-plates.
•A nonlinear numerical model functionally graded carbon nanotube reinforced composite (FG-CNTRC) micro-plate.•Modified couple stress theory (MCST) coupled with trigonometric shear deformation theory coupled with isogeometric analysis.•Influence of damping characteristic on the oscillation of FG-CNTRC micro-plates.
•We investigate an inverse trigonometric shear deformation theory (ITSDT) for FGM isotropic and sandwich plates.•Isogeometric analysis (IGA) is used for static, free vibration and buckling analysis ...of plates.•Using IGA achieves easily C1-continuity generalized displacements.•Comparison is made with several other published methods.
A generalized shear deformation theory for static, dynamic and buckling analysis of functionally graded material (FGM) made of isotropic and sandwich plates is presented in this paper. Two new distribution functions are proposed in the present formulation. These functions determine the distribution of the transverse shear strains and stresses across the thickness of the plates. The present theory is derived from the classical plate theory (CPT), and hence the shear locking phenomenon can be ignored. It has same number of degrees of freedom as the first order shear deformation theory (FSDT), but it does not require shear correction factors because the shear stress free surface conditions are naturally satisfied. As demonstrated in the following sections, the proposed theory yields very accurate prediction for displacement, stresses, natural frequencies and critical buckling load compared to three-dimensional (3D) elasticity solution. Galerkin weak form of static, free vibration and buckling models for FGM isotropic and sandwich plates are used to create the discrete system of equations. This weak form requires C1-continuity for generalized displacements. It can be solved by a number of methods such as analytical methods, finite element methods based on the Hermite interpolation functions, meshfree method and recently developed NURBS based isogeometric analysis (IGA). The NURBS basis functions used in IGA are Cp−1 continuous and therefore can easily satisfy the C1-continuity condition. Numerical examples are presented to illustrate the effectiveness of the proposed method compared to other methods reported in the literature.
We present a generalized shear deformation theory in combination with isogeometric (IGA) approach for nonlinear transient analysis of smart piezoelectric functionally graded material (FGM) plates. ...The nonlinear transient formulation for plates is formed in the total Lagrange approach based on the von Kármán strains, which includes thermo-piezoelectric effects, and solved by Newmark time integration scheme. The electric potential through the thickness of each piezoelectric layer is assumed to be linear. The material properties vary through the thickness of FGM according to the rule of mixture and the Mori–Tanaka schemes. Various numerical examples are presented to demonstrate the effectiveness of the proposed method.
Equilibrium and stability equations of functionally graded material (FGM) plate under thermal environment are formulated in this paper based on isogeometric analysis (IGA) in combination with ...higher-order shear deformation theory (HSDT). The FGM plate is made by a mixture of two distinct components, for which material properties not only vary continuously through thickness according to a power-law distribution but also depend on temperature. Temperature field is assumed to be constant in plate surfaces and uniform, linear and nonlinear through plate thickness, respectively. The governing equation is in nonlinear form based on von Karman assumption and thermal effect. A NURBS-based isogeometric finite element formulation is capable of naturally fulfilling the rigorous C1-continuity required by the present plate model. Influences of gradient indices, boundary conditions, temperature distributions, material properties, length-to-thickness ratios on the behavior of FGM plate are discussed in details. Numerical results demonstrate excellent performance of the present approach.
An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap (DSG) technique using triangular meshes (ES-DSG) was recently proposed to enhance the accuracy of the existing ...FEM with the DSG for analysis of isotropic Reissner/Mindlin plates. In this paper, the ES-DSG is further formulated for static, free vibration and buckling analyses of functionally graded material (FGM) plates. The thermal and mechanical properties of FGM plates are assumed to vary across the thickness of the plate by a simple power rule of the volume fractions of the constituents. In the ES-DSG, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains associated with the edges of the elements. The present formulation uses only linear approximations and its implementation into finite element programs is quite simple. Several numerical examples are given to demonstrate the performance of the present formulation for FGM plates.
We present in this paper a simple and effective approach that incorporates isogeometric finite element analysis (IGA) with a refined plate theory (RPT) for static, free vibration and buckling ...analysis of functionally graded material (FGM) plates. A new inverse tangent distributed function through the plate thickness is proposed. The RPT enables us to describe the non-linear distribution of shear stresses through the plate thickness without any requirement of shear correction factors (SCF). IGA utilizes basis functions namely B-splines or non-uniform rational B-splines (NURBS) which reach easily the smoothness of any arbitrary order. It hence satisfies the C1 requirement of the RPT model. The present method approximates the displacement field with four degrees of freedom per each control point allowing an efficient solution process.
A novel and effective formulation that combines the eXtended IsoGeometric Approach (XIGA) and higher-order shear deformation theory (HSDT) is proposed to study the free vibration of cracked ...functionally graded material (FGM) plates. Herein, the general HSDT model with five unknown variables per node is applied for calculating the stiffness matrix without needing shear correction factor (SCF). In order to model the discontinuous and singular phenomena in the cracked plates, IsoGeometric Analysis (IGA) utilizing the Non-Uniform Rational B-Spline (NURBS) functions is incorporated with enrichment functions through the partition of unity method. NURBS basis functions with their inherent arbitrary high order smoothness permit the C1 requirement of the HSDT model. The material properties of the FGM plates vary continuously through the plate thickness according to an exponent function. The effects of gradient index, crack length, crack location, length to thickness on the natural frequencies and mode shapes of simply supported and clamped FGM plate are studied. Numerical examples are provided to demonstrate the performance of the proposed method. The obtained results are in close comparison with other published solutions in the literature.
•We analyze free vibration of functionally graded plates containing cracks.•The method is derived from higher-order shear deformation theory (HSDT) and extended isogeometric analysis (XIGA).•The proposed formulation fulfills high-continuity generalized displacements.•Numerical results show excellent performance of the proposed approach.
In this paper, we present an effectively numerical approach based on isogeometric analysis (IGA) and higher-order shear deformation theory (HSDT) for geometrically nonlinear analysis of laminated ...composite plates. The HSDT allows us to approximate displacement field that ensures by itself the realistic shear strain energy part without shear correction factors (SCFs). IGA utilizing basis functions namely B-splines or non-uniform rational B-splines (NURBS) enables to satisfy easily the stringent continuity requirement of the HSDT model without any additional variables. The nonlinearity of the plates is formed in the total Lagrange approach based on the small strain assumptions. Numerous numerical validations for the isotropic, orthotropic, cross-ply and angle-ply laminated plates are provided to demonstrate the effectiveness of the proposed method.
•An effectively numerical approach for geometrically nonlinear analysis of composite plates.•The method is derived from higher-order shear deformation theory (HSDT) and isogeometric analysis (IGA).•NURBS basis functions possess C1 continuity required by HSDT.•Numerical results show good performance of the present method.
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