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横向剪切变形对复合材料层合板弯曲与振动的影响甚大。在本文的近似分析中,假定板在弯曲时横向位移沿整个板厚为常量。横向剪切应变沿各层厚度方向也分别为常量,但各层不同。文中以特殊正交各向异性层合板为例,采用两种不同的方法建立了各层剪切应变间的关系,推演了层合板横向弯曲与振动的微分方程组及边界条件。算例表明,即使层合板的跨——厚比很小,用本文两种分析方案计算位移、应力及固有频率,都仍具有较高的精度。
Lateral shear deformation has a great influence on the bending and vibration of composite laminates. In the approximate analysis of this paper, it is assumed that the lateral displacement of the plate during bending is constant along the entire plate thickness. The transverse shear strain is also constant along the thickness of each layer, but the layers are different. Taking a special orthogonal anisotropic laminate as an example, two different methods are used to establish the relationship between the shear strains of different layers and the differential equations and the boundary conditions of transverse bending and vibration of the laminate are deduced. The examples show that even though the span-to-thickness ratio of the laminates is small, the accuracy of displacement, stress and natural frequency can be calculated using the two analysis schemes in this paper.