Viscoelastic Composite Plate Considering Damage Effects Nonlinear Static, Dynamic Analysis

By considering the influence of damage, viscoelasticity and geometric nonlinearity synthetically, the actual state of composite material and structure can be described accurately and the essential character of the mechanics property can be revealed fully. In the present, the research achievement of this field is much few. The main reasons are as follows: (l)the establishment of the constitutive equations for the viscoelastic composite with damage is much difficulty. (2)the governing equations will increase and are complicated when damage variable is introduced. (3)generally, the governing equations are integral- partial differential equations, further more, because damage variable is coupling with stress and strain, Galerkin method is no longer suitable, it is quite difficult to solve the equations.In this paper, the nonlinear static and dynamic behavior of the composite viscoelastic plate with growing damage is investigated. The effects of damage and viscoelasticity on the nonlinear dynamic response and postbuckling character of the composite plate are analysed. At the same time, a general method for analysing and solving this type problem are studied. The main researching contents and results are as follows: The nonlinear dynamic response of viscoelastic elliptical plate with differential constitutive relation is investigated by applying KBM method, and the results show that viscoelasticity exhibits damping property in dynamic system. For the nonlinear dynamic problems of the viscoelastic structure, in which the constitutive relation is integral form and relaxed modulus are Prony series form, based on the Newmark method and Newton-Cotes numerical integration method, a new numerical approach is established, and by using this approach the abundant dynamic behaviors of viscoelastic structure are obtained. Based on Schapery three-dimensional viscoelastic constitutive with growing damage, through introducing Shenwei and Kachanov damage evolution equation, a damage model with matrix transverse cracks for the viscoelastic unidirectional laminated composite is established. By synthetically applying finite difference method, Newmark method and Newton-Cotes numerical integration formula, the integral- partial differential governing equations are solved. For the viscoelastic unidirectional laminatedcomposite under transverse periodic loading, the effects of damage on the nonlinear dynamic responses are investigated. For the viscoeiastic fibre reinforced unidirectional composite structure with initial deflection under compression load in plane, the effects of damage on the postbuckling behaviors are analysed. The research results indicate that transverse crack will cause a decrease of the structure's rigidity and an increase of the deflection, but not lead to the whole structure's failure.