Finite element analysis of anisotropic viscoelastic composite structures and analytical determination of optimum viscoelastic material properties

Quasi-static linear anisotropic viscoelastic responses of composite structures subjected to mechanical and hygrothermal loads are formulated in terms of finite element algorithms. Laplace and/or Fourier transforms rather than direct time integrations are used in this formulation in order to improve accuracy and to save extensive computational time and storage. The present quasi-static viscoelastic analyses require the same computer memory as is needed for corresponding elastic eigenvalue problems. Bending and stretching of composite plates for which analytical solutions exist are examined in order to evaluate the accuracy and effectiveness of the present approach. The time dependent displacement fields in the transverse direction for the cross ply and angle ply laminates are calculated and the stacking sequence effects of the laminates are discussed in detail. Creep responses for GY70/339 composite laminates with or without a circular hole are also studied. The numerical results compare favorably with analytical solutions, i.e. within 1.8% for bending and 10{dollar}sp{lcub}-3{rcub}{dollar}% for tension.; Numerical procedures for analyzing dynamic responses of composite structures with time, temperature and moisture dependent linear viscoelastic damping also have been developed in the time domain using variational principles and the Newmark average acceleration method. Recursion formulas have been formulated in order to reduce computer storage and only the previous time solution is required to compute the next time solution. Verification studies were conducted to evaluate the accuracy and convergence of the present numerical algorithm and they show that the numerical solutions agree well with the analytical ones. As examples, the dynamic transient responses of long cantilevered T300/934 composite Euler beams subjected to unit step and impulse loads were calculated using the presently developed procedures.; By using generalized Maxwell models, expressions for stored and dissipated energies in anisotropic viscoelastic bodies are derived. The relaxation modulus curves are analytically generated for parameters such as the initial modulus, the fully relaxed equilibrium modulus, the slope of the transition region and the time span of the relaxation. The influences of relaxation modulus shapes and parameters on stored and dissipated energies under specific loads are then analyzed. By using the present finite element methods, the dynamic transient response of cantilever beams with free damping layers on both sides is calculated in order to evaluate performance of free layer damping treatments.