Mohammad Tawfik

Thermal post-buckling and aeroelastic behaviour of shape memory alloy reinforced plates

A novel concept is proposed: the use of shape memory alloy (SMA) to reduce panel thermal deflection and flutter responses. SMA has a unique ability to recover large pre-strains completely when the alloy is heated above the austenite finish temperature Af. The transformation austenite start temperature As for nitinol can be anywhere between -60 °F (-50 °C) and +340 °F (+170 °C) by varying the nickel content. During the recovery process, a large tensile recovery stress occurs if the SMA is restrained. The shape memory effect phenomenon is attributed to a change in crystal structure known as a reversible austenite to martensite phase transformation. This solid-solid phase transformation also gives a large increase in Youngs modulus and yield stress. In this paper, a panel subject to the combined aerodynamic and thermal loading is investigated. A nonlinear finite element model based on the von Karman strain-displacement relation is utilized to study the effectiveness of an SMA-embedded panel on the flutter boundary, critical buckling temperature, post-buckling deflection and free vibration. The study is performed on an isotropic panel with embedded SMA. The aerodynamic model is based on the first-order quasi-steady piston theory. The dynamic pressure effect on the buckling and post-buckling behaviour of the panel is investigated by introducing the aerodynamic stiffness term, which changes the critical buckling temperature. Panels with SMA embedded in either the longer or shorter direction and either fully or partially embedded are investigated for post-buckling behaviour. Similarly, the influence of temperature elevation on the flutter boundary and vibration frequencies is investigated.

Thermal Buckling and Nonlinear Flutter Behavior of Functionally Graded Material Panels

The nonlinear flutter and thermal buckling of an functionally gradient material panel under the combined effect of elevated temperature conditions and aerodynamic loading is studied. A nonlinear finite element model based on the first-order shear deformable plate theory and von Karman strain-displacement relations is adopted. The governing nonlinear equations are obtained using the principal of virtual work, adopting an approach based on the thermal strain being a cumulative physical quantity to account for temperature-dependent material properties. The aerodynamic pressure is modeled using the quasi-steady first-order piston theory. This system of nonlinear equations is solved by the Newton-Raphson numerical technique. It is found that the temperature increase has an adverse effect on the functionally gradient material panel flutter characteristics through decreasing the critical dynamic pressure. Decreasing the volume fraction enhances flutter characteristics, but this is limited by structural integrity aspect. The presence of aerodynamic flow results in postponing the buckling temperature and in suppressing the postbuckling deflection, and the temperature increase gives way for higher limit-cycle amplitude.

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.

Analysis and control of large thermal deflection of composite plates using shape memory alloy

A finite element method for predicting critical temperature and postbuckling deflection is presented for composite plates embedded with prestrained shape memory alloy (SMA) wires and subjected to high temperatures. The temperature- dependent material properties of SMA and matrix, and the geometrical non linearities of large deflection are considered in the formulation. An incremental method consisting of small temperature increments and including the effect of initial deflection and initial stresses for materials non linearities is presented. Within each temperature increment, the Newton-Raphson iteration method is used for calculating large thermal deflection. Results show that the critical buckling temperature can be raised high enough and the postbuckling deflection can be reduced and controlled for a given operating temperature range by the proper selection of SMA volume fraction, prestrain and alloy composition.

Suppression of postbuckling deflection and panel flutter using shape memory alloy

A novel concept proposed is the use of SMA to reduce the panel thermal deflection and linear flutter responses. SMA has the unique ability of recovering large prestrain completely when the alloy is heated. During the recovery process, a large tensile recovery stress occurs if the SMA is restrained. In this paper, a panel subject to the combined aerodynamic and thermal loading is investigated. A nonlinear finite element model based on von Karman strain displacement relation is utilized to study the effectiveness of an SMA embedded panel on the flutter boundary, critical buckling temperature and post-buckling deflection. The study is performed on an isotropic panel, with embedded SMA. The aerodynamic model is based on the first order quasi-steady piston theory. The aerodynamic pressure effect on the buckling and post-buckling behavior of the panel is investigated by introducing the aerodynamic stiffness term, which changes both the critical buckling temperature and the post-buckling shape. Panels with SMA embedded in either x or y-direction and either partially or fully embedded are investigated for post-buckling behavior. Similarly, the influence of the temperature elevation on the flutter boundary is investigated by including the thermal terms.

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.

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.

Vibration of laminated composite plates embedded with shape memory alloy at elevated temperatures

A finite element formulation and solution procedure for the free vibration behavior of composite plates with embedded shape memory alloy (SMA) at elevated temperatures is presented. The temperature-dependent material properties of MA and composite matrix, and the geometrical nonlinearity due to large thermal deflection are considered in the formulation. The solution procedure consists of two steps: large thermal deflection is determined first, then followed by the free vibration analysis about the thermally buckled equilibrium position. Examples of hybrid composite plates are given to show the variation of lowest few frequencies versus temperature and the influence of SMA on the natural frequencies at elevated temperatures. Potential applications to frequency turning and sonic fatigue using SMA are discussed.

Aerothermoacoustic Response of Shape Memory Alloy Hybrid Composite Panels

theacousticexcitationisconsideredtobeawhite-Gaussianrandompressurewithzeromeananduniformmagnitude over the panel surface. Nonlinear temperature-dependence of material properties is considered in the formulation. The dynamic nonlinear equations of motion are transformed to modal coordinates to reduce the computational efforts. The Newton–Raphson iteration method is employed to obtain the dynamic response at each time step of the Newmark numerical integration scheme. Finally, the nonlinear response of a shape memory alloy hybrid composite panel is presented, illustrating the effect of shape memory alloy fiber embeddings, aerodynamic pressure, sound pressure level, and temperature rise on the panel response.

Dynamics and Stability of Stepped Gun-Barrels with Moving Bullets

The stability of an Euler-Bernoulli beam under the effect of a moving projectile will be reintroduced using simple eigenvalue analysis of a finite element model. The eigenvalues of the beam change with the mass, speed, and position of the projectile, thus, the eigenvalues are evaluated for the system with different speeds and masses at different positions until the lowest eigenvalue reaches zero indicating the instability occurrence. Then a map for the stability region may be obtained for different boundary conditions. Then the dynamics of the beam will be investigated using the Newmark algorithm at different values of speed and mass ratios. Finally, the effect of using stepped barrels on the stability and the dynamics is going to be investigated. It is concluded that the technique used to predict the stability boundaries is simple, accurate, and reliable, the mass of the barrel on the dynamics of the problem cannot be ignored, and that using the stepped barrels, with small increase in the diameter, enhances the stability and the dynamics of the barrel.