Supersonic flutter of laminated thin plates with thermal effects

Abstract

A 48 degree-of-freedom rectangular laminated thin plate finite element including the effects of thermal and aerodynamic loadings is formulated to study the buckling and supersonic flutter characteristics of thin plate structures. Interactive effects between the critical temperature difference and critical aerodynamic pressure for the plates are also studied. The element formulation is based on the classical lamination theory. The aerodynamic pressure due to supersonic potential flow is described by a two-dimensional steady supersonic theory. The element formulation and solution procedure are evaluated by comparing results of three examples with existing alternative solutions. The practical applicability is demonstrated by performing buckling and supersonic flutter analyses of laminated thin plates under various types of temperature distributions. Based on the numerical results, the effects of aspect ratio, ratio of thermal expansion coefficients, fiber orientation, type of temperature distribution, and flow angularity on these examples are discussed. HIN plates are a popular and useful form of structural components with significant applications in aerospace ve- hicles, such as high-speed aircraft, rocket, and spacecraft, which are subjected to thermal loads due to aerodynamic and/ or solar radiation heating. This results in a temperature dis- tribution over the surface and thermal gradient through the thickness of the plate. Due to boundary constraints, com- pressive stresses are induced and may cause buckling. There- fore, thermal buckling is a significant failure mode governing the design of thin plates used in aerospace structures. For obvious advantages such as the high-strength-to-weight ratio and high-stiffness-to-weight ratio, etc., fiber-reinforced laminated composite materials have been increasingly used in the design and fabrication of thin plate structures. It is of interest to briefly review the works done in thermal buckling of laminated composite plates. For example, Whit- ney and Ashton1 studied the thermal buckling of symmetric, angle-ply, layered composite plates with simply supported edges using energy formulation. The critical temperatures for plates with various types of composite were presented. Chen and Chen2 analyzed the thermal buckling of laminated cylin- drical panels using Galerkin's method. The critical temper- atures for plates with various structural and material param- eters, and boundary conditions were presented. Tauchert and Huang3 investigated thermal buckling of simply supported symmetric angle-ply laminated plates under uniform temper- ature change using the Rayleigh-Ritz method. The critical temperature and associated mode shape for plates with var- ious fiber orientations, numbers of layers, and aspect ratios were presented. Thangaratnam et al. 4 studied the thermal buckling of composite laminated plates using semiloof finite elements. The critical temperatures for plates under various types of temperature distribution, lamination parameters, and boundary conditions were presented. Chen and Chen5 ana- lyzed the thermal buckling of laminated cylindrical plates sub- jected to a nonuniform temperature field using the finite ele- ment method. The critical temperatures for the plates with various lamination angle, modulus ratio, number of layers, plate aspect ratio, and boundary condition were presented.