Static and Vibration Analyses of General Wing Structures Using Equivalent-Plate Models

An efficient method, using equivalent plate model, is developed for studying the static and vibration analyses of general built-up wing structures composed of skins, spars, and ribs. The model includes the transverse shear effects by treating the built-up wing as a plate following the Reissner-Mindlin theory, the so-called First-order Shear Deformation Theory (FSDT). The Ritz method is used with the Legendre polynomials being employed as the trial functions. This is in contrast to previous equivalent plate model methods which have used simple polynomials, known to be prone to numerical ill-conditioning, as the trial functions. The present developments are evaluated by comparing the results with those obtained using MSC/NASTRAN, for a set of examples. These examples are: (i) free-vibration analysis of a clamped trapezoidal plate with (a) uniform thickness, and (b) non-uniform thickness varying as an airfoil, (ii) free-vibration and static analyses (including skin stress distribution) of a general built-up wing, and (iii) free-vibration and static analyses of a swept-back box wing. The results obtained by the present equivalent plate model are in good agreement with those obtained by the finite element method.

[1]  Gary L. Giles,et al.  Equivalent plate modeling for conceptual design of aircraft wing structures , 1995 .

[2]  Norman F. Knight,et al.  On a consistent first-order shear-deformation theory for laminated plates , 1997 .

[3]  Ahmed K. Noor,et al.  Continuum Modeling for Repetitive Lattice Structures , 1988 .

[4]  Rakesh K. Kapania,et al.  Recent advances in analysis of laminated beams and plates. Part I - Sheareffects and buckling. , 1989 .

[5]  Usik Lee,et al.  DYNAMIC CONTINUUM MODELING OF BEAMLIKE SPACE STRUCTURES USING FINITE ELEMENT MATRICES , 1990 .

[6]  E. Reissner.  The effect of transverse shear deformation on the bending of elastic plates , 1945 .

[7]  Antonio Miravete,et al.  Practical Analysis of COMPOSITE LAMINATES , 2018 .

[8]  Rakesh K. Kapania,et al.  A Simple Element for Aeroelastic Analysis of Undamaged and Damaged Wings , 1989 .

[9]  Rakesh K. Kapania,et al.  Free vibration of thick generally laminated cantilever quadrilateral plates , 1996 .

[10]  Usik Lee,et al.  Dynamic Continuum Plate Representations of Large Thin Lattice Structures , 1993 .

[11]  Rakesh K. Kapania,et al.  Analytical shape sensitivities and approximations of modal response of generally laminated tapered skew plates , 1992 .

[12]  Adnan H. Nayfeh,et al.  Continuum modeling of the mechanical and thermal behavior of discrete large structures , 1981 .

[13]  Rakesh K. Kapania,et al.  Free Vibration of Thick Generally Laminated Quadrilateral Plates Having Arbitrarily Located Point Supports , 1998 .

[14]  Melvin S. Anderson,et al.  Continuum Models for Beam- and Platelike Lattice Structures , 1978 .

[15]  Gary L. Giles,et al.  Equivalent plate analysis of aircraft wing box structures with general planform geometry , 1986 .

[16]  Rakesh K. Kapania,et al.  Free vibration analyses of generally laminated tapered skew plates , 1992 .

[17]  Silvano Tizzi,et al.  Numerical Procedure for the Dynamic Analysis of Three-Dimensional Aeronautical Structures , 1997 .

[18]  Eli Livne,et al.  Nonlinear Equivalent Plate Modeling of Wing-Box Structures , 1999 .

[19]  Eli Livne,et al.  Equivalent plate structural modeling for wing shape optimization including transverse shear , 1994 .