Abstract: This paper employs the best approximation of part series sum of normal polynomials. and proposes a new method with the Fourier-Hermite polynomial expansion expressing structural dynamic responses. Analytic expressions of displacement and velocity responses of vibrational systems are e stablished in this paper, and stability condition of the step-by-step algorithm is discussed. Finally, a computational example is demonstrated, and the precision of its results is compared with conventional methods.

Key words: shape memory alloys, phase transformation, superelasticity, large deformation, finite element