板结构计算模型的新发展

New development of the computational model for the analysis of laminated plate structures

现代复合材料层合板具有高强和轻型的突出优点,从而在军工和民用等诸多领域发挥着重要作用。这种板结构的特点是随着纤维走向的不同,层间材料的物理-力学特性发生剧烈变化。沿板厚方向变形的梯度比较陡峭,并在层间结合面处发生强不连续,呈现zig-zag(锯齿状)现象。这导致横向剪应变在板的静态和动态响应中发生重要作用,不计横向变形的经典组合板计算模型CLPT难以适应现代多层板计算分析的需要。考虑横向剪切变形影响的板的计算模型得到重视和发展。需要指出,现有各种考虑剪切变形影响的计算模型虽然有了很大的发展,但在全面和准确性上仍然存在一定的不足,难以适应现代多层组合板横向力和物理性能多变的情况。模型预测的沿板厚方向位移和应力的变化规律难以通过严格的检验。本文提出的以比例边界有限元为基础的正交各向异性板的数值计算模型,同时可适用于各种薄板与厚板的分析,对现代复合材料层合板的分析具有特殊的优越性。所得到的板的位移、正应力和剪应力沿板厚方向的变化,与三维弹性理论的标准解高度吻合。数值算例进一步表明,随着层间纤维走向的变化,板内位移场和应力场沿板厚方向剧烈变化所呈现的锯齿现象均可以精准地进行模拟。据此,本文建议方法对现代板分析的广泛适应性和高度准确性得到了充分论证。

Modern laminated composite plates have distinguished advantages,such that they play a significant role in many fields of military and civil engineering applications.This kind of plates is characterized by quite different mechanical-physical properties in the thickness direction with the change of fiber orientation.The slopes of transverse displacements exhibit strong discontinuous change at the layer interfaces,which is well known as the zig-zag phenomenon.As a result,the transverse shear strain plays an important role in the plate response.Thus,the classical laminate plate theory is inadequate for the analysis of multilayer composites,while the theories which account for shear deformation effects attract researchers to be pay attention to and are developed.It is worth to note,over the past decades,although numerous models considering shear deformation effects have been developed for the solution of laminate plates and great achievements have been made,there are still some deficiencies in the versatility and accuracy of these models.They have difficulties to meet the requirements of myriad changes of mechanical-physical properties of modern laminate composite plates,the predicted displacement and stress fields along the thickness direction can hardly pass the stringent test.In this paper,an approach based on the scaled boundary finite element method(SBFEM)for the numerical analysis of orthotropic laminated composite plates is developed,which is equally applicable to the analysis of thin and thick plates.Numerical examples of orthotropic laminated composite plates show that highly accurate results can be achieved,the predicted displacement and stress fields agree very well with those obtained by the exact solutions of 3D theory of elasticity.Furthermore,the numerical examples demonstrate that the phenomena of the zig-zag distribution of the displacement and stress fields through the plate thickness can be accurately simulated.Accordingly,the versatility and perfect accuracy of the proposed approach are fully validated.