Thermal Post-buckling Deflection Research Articles

Isogeometric thermal postbuckling of FG-GPLRC laminated plates

An analysis on thermal buckling and postbuckling of composite laminated plates reinforced with a low amount of graphene platelets is performed in the current investigation. It is assumed that graphaene platelets are randomly oriented and uniformly dispersed in each layer of the composite media. Elastic properties of the nanocomposite media are obtained by means of the modified Halpin-Tsai approach which takes into account the size effects of the graphene reinforcements. By means of the von Karman type of geometrical nonlinearity, third order shear deformation theory and nonuniform rational B-spline (NURBS) based isogeometric finite element method, the governing equations for the thermal postbuckling of nanocomposite plates in rectangular shape are established. These equations are solved by means of a direct displacement control strategy. Numerical examples are given to study the effects of boundary conditions, weight fraction of graphene platelets and distribution pattern of graphene platelets. It is shown that, with introduction of a small amount of graphene platelets into the matrix of the composite media, the critical buckling temperature of the plate may be enhanced and thermal postbuckling deflection may be alleviated.

Thermal post-buckling of temperature dependent sandwich plates with FG-CNTRC face sheets

ABSTRACTPresent research investigates the thermal postbuckling of sandwich plates containing a stiff core and two thin carbon nanotube reinforced composite (CNTRC) face sheets. Properties of the core, carbon nanotubes (CNTs) and polymeric matrix of the faces are assumed to be temperature-dependent. It is assumed that CNTs as reinforcements may be distributed according to a functionally graded pattern. Plate is formulated based on the first-order shear deformation theory and von Kármán type of geometrical nonlinearity. The governing equations are obtained by the energy method with the aid of the Conventional Ritz method. Shape functions of the Ritz method are estimated according to the Chebyshev polynomials. A set of nonlinear eigenvalue equations is achieved. The obtained equations are homogeneous, coupled, and nonlinear in terms of both displacements and temperature. A successive displacement control strategy is implemented to trace the thermal postbuckling equilibrium path of the plate. It is shown that, with increasing the volume fraction of CNT, critical buckling temperature of sandwich plate increases and postbuckling deflection decreases. Furthermore, through a functionally graded distribution of volume fraction of CNTs across the thickness, critical buckling temperature of the sandwich plate may be enhanced and thermal postbuckling deflection may be alleviated.

Enhancement of non-linear thermal stability of temperature dependent laminated beams with graphene reinforcements

Present investigation deals with the thermal postbuckling behaviour of a composite laminated beam where graphene is used as reinforcement of each lamina. The composite laminated beam may be piecewise functionally graded by changing the volume fraction of graphene in each lamina. Mechanical properties in each layer are obtained according to the modified Halpin-Tsai approach which contains efficiency parameters to capture the size dependency of the nanocomposite properties. Thermomechanical properties of the matrix and reinforcements are assumed to be temperature dependent. Beam is resting on an elastic foundation which acts in compression as well as in tension. The first order shear deformation beam theory and von Kármán type of geometrical nonlinearity are used as the basic assumptions to establish the total strain energy of the system. Beam is subjected to uniform temperature elevation. With the aid of conventional Ritz method and the simple polynomials as the basic functions, the matrix representation of the governing equations is derived. The adopted solution method may be used for arbitrary combinations of boundary conditions. The obtained system of equations is nonlinear in terms of both temperature and displacements. An iterative displacement control strategy is proposed to extract the thermal postbuckling curves of the beam resting on a conventional elastic foundation. Numerical results are given to discuss the effects of graphene distribution, stacking sequence, boundary conditions, side to thickness ratio and foundation stiffness on critical buckling temperature and thermal postbuckling equilibrium path of the beam. It is shown that, through a piecewise functionally graded distribution of graphene in matrix, critical buckling temperature may be enhanced significantly and thermal postbuckling deflection may be alleviated.

Enhanced thermal stability of functionally graded sandwich cylindrical shells by shape memory alloys

The present paper deals with the nonlinear thermal instability of geometrically imperfect sandwich cylindrical shells under uniform heating. The sandwich shells are made of a shape memory alloy (SMA)-fiber-reinforced composite and functionally graded (FG) face sheets (FG/SMA/FG). The Brinson phenomenological model is used to express the constitutive characteristics of SMA fibers. The governing equations are established within the framework of the third-order shear deformation shell theory by taking into account the von Karman geometrical nonlinearity and initial imperfection. The material properties of constituents are assumed to be temperature dependent. The Galerkin technique is utilized to derive expressions of the bifurcation points and bifurcation paths of the sandwich cylindrical shells. Using the developed closed-form solutions, extensive numerical results are presented to provide an insight into the influence of the SMA fiber volume fraction, SMA pre-strain, core thickness, non-homogeneity index, geometrical imperfection, geometry parameters of sandwich shells and temperature dependency of materials on the stability of shells. The results reveal that proper application of SMA fibers postpones the thermal bifurcation point and dramatically decreases thermal post-buckling deflection. Moreover, the induced tensile recovery stress of SMA fibers could also stabilize the geometrically imperfect shells during the inverse martensite phase transformation.

Nonlinear thermal stability of geometrically imperfect shape memory alloy hybrid laminated composite plates

The instability of geometrically imperfect shape memory alloy (SMA) fibers reinforced with hybrid laminated composite (SMAHC) plates and subjected to a uniform thermal loading is analytically investigated. The material properties of the SMAHC plates are assumed to be functions of temperature. Nonlinear equations of the plates’ thermal stability are derived based on a higher order shear deformation theory incorporating von Karman geometrical nonlinearity via stationary potential energy. The structural recovery stress, which is generated by martensitic phase transformation of the prestrained SMA fibers, is calculated based on the one-dimensional thermodynamic constitutive model by Brinson. Adopting the Galerkin procedure, the governing nonlinear partial differential equations are converted into a set of nonlinear algebraic equations, in which systems of equations are solved by introducing an analytical approach. Closed-form formulations are presented to determine the load-deflection path and critical buckling temperature of the plate. Based on the developed closed-form solutions, ample numerical results are presented to provide an insight into the effects of the volume fraction, prestrain, location and orientation of the SMA fibers, composite plate geometry, geometrical imperfection and temperature dependence on the stability of the SMAHC plates. It is shown that a proper application of SMA fibers results in a considerable delay of the thermal bifurcation and controllable thermal post-buckling deflection of the SMAHC plate.

Nonlinear Response of Graphite-Epoxy Composite Thin-Walled Structure under Elevated Thermal Environment

Composite materials thin-walled structures are widely used as skin panel in flight vehicles in recent years. These structures will encounter severe complex loading conditions, which may be a combination of mechanical, aerodynamic, thermal and acoustic loads. Thin-walled structures subjected to this kind of loadings will exhibit nonlinear response; as a result, fatigue failure will occur. High temperature may cause large thermal deflection and stress, for some special conditions, may cause thermal buckling. Once the thermal buckling appears, the stiffness will change correspondingly, it will cause significant influence on the dynamic response and fatigue failure. Accordingly, it is important to research the nonlinear response of this kind of structures under elevated thermal environment. Nonlinear response and thermal pre-buckling/post-buckling behavior of a Graphite-Epoxy composite plate subjected to server thermal loading is numerically investigated in this paper. A composite laminated plate with clamped-clamped boundary conditions is chosen as simulated body, nonlinear finite element model is developed using the first-order shear deformable plate theory, Von Karman strain-displacement relations, and the principle of virtual work. The thermal load is assumed to be a steady-state with different predefined temperature distribution. The thermal strain is stated as an integral quantity of the thermal expansion coefficient with respect to temperature. Then the modes of the plate are analyzed, the nature frequencies and modal shapes are obtained. The critical temperature of buckling is calculated. The static nonlinear equations of motions are solved by the Newton-Raphson iteration technique to obtain the thermal post-buckling deflection. The Riks method is used to analyze static post-buckling behavior. In the numerical examples, four types of situations are studied, which include i) the buckling behaviors for different initial imperfections, ii) the buckling behaviors for different thickness to width ratios, and iii) The buckling behaviors for different width to length ratios; The critical temperature, the static thermal post-buckling deflection and the load to displacement relation are presented respectively. The influences of different boundary conditions on the buckling behaviors of the plate are achieved as well. The simulation method and results presented in this paper can be valuable references for further analysis of the nonlinear responses of thin-walled structures under complex loading conditions.

Thermal buckling and nonlinear flutter behavior of shape memory alloy hybrid composite plates

A new nonlinear finite element model is provided for the nonlinear flutter response of shape memory alloy (SMA) hybrid composite plates under the combined effect of thermal and aerodynamic loads. The nonlinear governing equations for moderately thick rectangular plates are obtained using first-order shear-deformable plate theory, von Karman strain-displacement relations and the principle of virtual work. To account for the temperature dependence of material properties, the thermal strain is stated as an integral quantity of thermal expansion coefficient with respect to temperature. The aerodynamic pressure is modeled using the quasi-steady first-order piston theory. Newton-Raphson iteration method is employed to obtain the thermal post-buckling deflection, while the linearized updated mode method is implemented in predicting the limit-cycle oscillation at elevated temperatures. Numerical results are presented to show the thermal buckling and flutter characteristics of SMA hybrid composite plates, illustrating the effect of the SMA volume fraction and pre-strain value on the aero-thermo-mechanical response of such plates.

Limit-cycle Oscillations of Functionally Graded Material Plates Subject to Aerodynamic and Thermal Loads

The nonlinear flutter and thermal buckling of a functionally graded material (FGM) plate panel subjected to combined thermal and aerodynamic loads are investigated using a finite element model based on the thin plate theory and von Karman strain-displacement relations to account for moderately large deflection. The thermal load is assumed to be steady-state constant temperature distribution, and the aerodynamic pressure is modeled using the quasi-steady first-order piston theory. The governing nonlinear equations of motion are obtained using the principle of virtual work adopting an approach based on the thermal strain being a cumulative physical quantity to account for temperature dependent material properties. The static nonlinear equations are solved by Newton-Raphson numerical technique to get the thermal post-buckling deflection. The dynamic nonlinear equations of motion are transformed to modal coordinates to reduce the computational efforts. The Newmark implicit integration scheme is employed to solve the second order ordinary differential equations of motion. Finally, the buckling temperature, post-buckling deflection and the nonlinear limit-cycle oscillations of an FGM panel are presented, illustrating the effect of volume fraction exponent, dynamic pressure, temperature rise, and boundary conditions on the panel response.

Limit-Cycle Oscillation of Shape Memory Alloy Hybrid Composite Plates at Elevated Temperatures

A traditional composite plate impregnated with pre-strained shape memory alloy fibers and subject to combined thermal and aerodynamic loads is investigated to demonstrate the effectiveness of using the SMA fiber embeddings in improving the static and dynamic response of composite plates. The problems investigated can be categorized into: thermal buckling subject to aerodynamic loading, linear flutter boundary at elevated temperatures, nonlinear flutter limit-cycle, and chaotic oscillations at elevated temperatures. A nonlinear finite element model based on the von Karman strain displacement relations and first-order shear deformable plate theory is derived. Aerodynamic pressure is modeled using the quasi-steady first-order piston theory. The governing equations are obtained using the principle of virtual work based on thermal strain being a cumulative physical quantity. Newton-Raphson iteration is employed to obtain the static aero-thermal large deflection at each temperature step and the dynamic response at each time step of the Newmark numerical integration scheme. A frequency domain solution is presented for predicting the flutter boundary at elevated temperatures, while the time domain method along with modal transformation is applied to numerically investigate periodic, non-periodic, and chaotic limit-cycle oscillations. The results show that the critical buckling temperature of the plate is greatly increased, and hence the thermal post-buckling deflection is suppressed by using SMA fiber embeddings. The SMA fiber embeddings caused an increase in the critical dynamic pressure at elevated temperatures, and enlargement of the static flat and dynamically stable region of the panel.

Thermoacoustic Random Response of Shape Memory Alloy Hybrid Composite Plates

Random dynamic response and thermal buckling of a shape memory alloy hybrid composite plate subjected to combined thermal and random acoustic loads are investigated. A nonlinear finite element model was developed using the first-order shear-deformable plate theory, von Karman strain-displacement relations, and the principle of virtual work. The thermal load was assumed to be a steady-state constant-temperature distribution, whereas the acoustic excitation was modeled as a white-Gaussian pressure with zero mean and uniform magnitude over the plate surface. To account for the nonlinear temperature dependence of material properties, the thermal strain was stated as an integral quantity of the thermal expansion coefficient with respect to temperature. The static nonlinear equations of motion are solved by the Newton-Raphson iteration technique to obtain the thermal postbuckling deflection, whereas the dynamic nonlinear equations of motion were transformed to modal coordinates and solved by employing Newmark implicit integration scheme. Finally, the critical buckling temperatures, static thermal postbuckling deflections, and random dynamic responses of a shape memory alloy hybrid-composite-plate panel are presented, illustrating the effect of shape memory alloy fiber embedding, sound pressure level, and temperature rise on the panel response.

RANDOM RESPONSE OF SHAPE MEMORY ALLOY HYBRID COMPOSITE PLATES SUBJECT TO WHITE-GAUSSIAN NOISE AND THERMAL ENVIRONMENT

The random response and thermal buckling of a traditional composite plate impregnated with pre-strained shape memory alloy (SMA) fibers subjected to combined thermal and acoustic loads are investigated using a finite element model based on the first order shear deformable plate theory and von Karman strain-displacement relations to account for moderately large deflection. The thermal load is assumed to be steady state constant temperature distribution, and the acoustic excitation is considered to be a stationary Gaussian pressure with zero mean and uniform magnitude over the plate surface. The governing nonlinear equations are obtained using the principal of virtual work adopting an approach based on the thermal strain being an integral quantity of the thermal expansion coefficient with respect to temperature to account for temperature dependent material properties. The static nonlinear equations are solved by Newton-Raphson numerical technique to get the thermal post-buckling deflection. The dynamic nonlinear equations of motion are transferred to modal coordinates to reduce the computational efforts. The Newmark implicit integration scheme is employed to solve the second order ordinary differential equations of motion. Finally, the buckling temperature, post-buckling deflection and the random response of a SMA hybrid composite plate panel are presented, illustrating the effect of SMA volume fraction, pre-strain, sound pressure level and temperature rise on the panel response.

Thermal post-buckling and flutter characteristics of composite plates embedded with shape memory alloy fibers

It is investigated that the composite plate embedded with shape memory alloy (SMA) fibers is subject to the aerodynamic and thermal loading in the supersonic region. The nonlinear finite element equations based on the first-order shear deformation plate theory (FSDT) are formulated for the laminated composite plate embedded with SMA fibers (SMA composite plate). The von Karman strain–displacement relation is used to account for the large deflection. The incremental method considering the influence of the initial deflections and initial stresses is adopted for the temperature-dependent material properties of SMA fibers and composite matrix. The first-order piston theory is used for modeling aerodynamic loads. This study shows the effect of the SMA on the critical temperature, thermal post-buckling deflection, natural frequency and critical dynamic pressure of the SMA composite plate.

A New Thermoelastic Model for Analysis of Shape Memory Alloy Hybrid Composites

A constitutive model and a finite element formulation are developed for predicting the thermomechanical response of SMA hybrid composite structures subjected to combined thermal and mechanical loads. The constitutive model is valid for constrained, restrained, or free recovery behavior with appropriate measurements of basic SMA material properties. The model captures the material nonlinearity of the SMA with temperature and more accurately captures the mechanics of composites with embedded SMA actuators as compared to other recently developed approaches. The constitutive and finite element models are amenable to commercial code implementation. The fundamental thermoelastic behavior of such structures is described in physical terms and related to the governing equations. It is shown that alloy selection is imperative for achieving the desired performance with respect to the application environment. It is also shown that fundamental efforts to strategically place actuators can produce dramatic performance improvements. Numerical results are shown for glass-epoxy beam specimens with embedded Nitinol actuators. Control of critical buckling temperature, thermal post-buckling deflection, and random response are demonstrated.