Efficient Numerical Aeroelastic Analysis of a High-Aspect-Ratio Wing Considering Geometric Nonlinearity

e1, e2, e3 = reference orthogonal unit vectors in the undeformed configuration e11, e12, e13 = strain vectors at the reference point e 1 , e 2 , e 3 = reference orthogonal unit vectors in the deformed configuration i1, i2, i3 = fixed orthogonal unit vectors 1, 2, 3 = strain curvature vectors in the undeformed configuration q = generalized nodal displacement vector T x1 = transformation matrix between a deformed-beam axis and a reference beam axis te x1 = transformation matrix between an undeformedbeam axis and a deformed-beam axis u, v, w = elastic displacements in the x, y, and z directions, respectively w1, w2, w3 = warping displacement = specific heat ratio