tailieunhanh - Some results in studying multilayered composite plates

This paper presents some results in studying the static and dynamic problems of multilayered composite plates, of which individual layer is made of unidirectional composite material. Calculations are based on the technical theory of laminar plates combined with using finite element method. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. :U, 1999, No 2 {89 - 98} SOME RESULTS IN STUDYING MULTILAYERED COMPOSITE PLATES PHAM TIEN DAT, NGUYEN HOA THINH Le Quy Don Technical University 1. Introduction Multilayered composite plates have wide applications in modern engineerings: civil engineering, transportation, aerospace, aviation, ocean engineering . At present, research problems are concentered on the calculation and design of composite structures, including: solution to static, dynamic and stability problems of multilayered composite structures; analysis of the affects of the connection and laminar alignments of materials on the plate working capacity; the optimization of structures of multilayered composite plates . This paper presents some results in studying the static and dynamic problems of multilayered composite plates, of which individual layer is made of unidirectional composite material. Calculations are based on the technical theory of laminar plates combined with using finite element method. 2. Formulation of the problem and method of solution Consider an-layered thin plate of which every laminar is composed of unidirectional composite materials (). z X We have a general vibration equation: [M]{q} + [C]{q} + [K]{q} = {F(t)}. 89 () For the problem of free vibration, without damping, () can be written as: [M]{q} + [K]{q} (} = 0. For the static problem, the equilibrium equation is of the form: (} [K]{q} = F where [M], [C), [K)- the mass, damping and stiffness matrices of plate, respectively; {q}, {q}, {q}- the vectors of nodal displacements, velocities and accelerations, respectively. {F(t)} -the nodal force vector. To solve the above problems, matrices [K], [M), (C) must be defined. These matrices are built on stiffness matrix [Ke), mass matrix [Me) of element. Using rectangular elements for composite plate problems (Fig. 2), at node i there are five degrees of freedom: {q} i = { UiViWi!p~cpn .