Beams resting on elastic foundations are widely used in engineering design such as railroad tracks, pipelines, bridge decks, and automobile frames. Laminated composite beams can be tailored for specific design requirements and offer a desirable design framework for beams resting on elastic foundations. Therefore, the analysis of flexural behaviour of laminated composite beams on elastic foundations is of important consequence. Exact solutions for flexural deflection of composite beams with coupling terms between stretching, shearing, bending and twisting, resting on two-parameter elastic foundations for various types of loading and boundary conditions, are presented for the first time. The proposed new formulation is based on Euler–Bernoulli beam theory having four degrees of freedom, namely bending in two principal directions, axial elongation and twist. Governing equations and boundary conditions are derived from the principle of virtual work and expressed in a compact matrix–vector form. By decoupling bending in both principal directions from twist and axial elongation, the fourth-order differential equation for bending is derived and transformed into a system of first-order differential equations. An exact solution of this system of equations is obtained using a fundamental matrix approach. Fundamental matrices for different configurations of elastic foundation are provided. The ability of the presented mathematical model in predicting flexural behaviour of beams on elastic foundations is verified numerically by comparison with results available in the literature. In addition, the deflection of anisotropic beams is analysed for different types of stacking sequences, boundary and loading conditions. The effect of elastic foundation coefficients on the flexural behaviour is also investigated and discussed.

搁置在弹性地基上的梁广泛用于工程设计中，例如铁轨，管道，桥面和汽车框架。层压复合梁可根据特定设计要求进行定制，并为弹性基础上的梁提供理想的设计框架。因此，在弹性地基上分析层压复合梁的抗弯性能具有重要意义。首次提出了基于组合梁在拉伸，剪切，弯曲和扭曲之间的耦合项的挠曲挠度的精确解，该解基于两参数弹性基础，针对各种类型的载荷和边界条件。拟议的新公式基于欧拉-伯努利梁理论，具有四个自由度，即在两个主要方向上弯曲，轴向伸长和扭曲。控制方程和边界条件是从虚拟工作原理导出的，并以紧凑的矩阵-向量形式表示。通过将两个方向上的弯曲与扭转和轴向伸长解耦，可以得出弯曲的四阶微分方程，并将其转换为一阶微分方程组。使用基本矩阵方法可以获得该方程组的精确解。提供了用于弹性地基的不同构造的基本矩阵。通过与文献中可用的结果进行比较，对所提出的数学模型预测梁在弹性地基上的弯曲行为的能力进行了数值验证。此外，还针对不同类型的堆叠序列分析了各向异性光束的挠度，边界和加载条件。还研究和讨论了弹性地基系数对弯曲行为的影响。