Laminated composite materials consist of oriented plies usually bonded together to provide desirable mechanical properties such as high stiffness and strength to weight ratio. The result is a feasible solution for many technological problems, principally in the naval, aerospace, and automotive industries. Laminated composite beams have been represented in many mathematical models since 3D elasticity to laminated beam theories such as discrete-layer approaches and equivalent single-layer models (ESL). In this article, the mathematical steps for deriving the fundamental solutions and integral equations of an ESL model, called first-order laminated composite beam theory (FOBT), under static loading are presented. The direct boundary element method (BEM) solution is properly addressed, incorporating topics such as: (a) explicit forms of influence matrices, (b) load vectors for concentrated loading and (trapezoidal, sinusoidal) distributed loading, and (c) reduction of BEM solution to the classical laminated beam theory. Numerical results are presented for beams under different static load cases, boundary conditions, and domain discontinuity problems associated with stepped beams and continuous beams. The results suggest the correctness and effectiveness of this direct BEM formulation.

层压复合材料由通常粘合在一起以提供所需机械性能（例如高刚度和强度重量比）的定向层组成。结果是解决许多技术问题的可行解决方案，主要是在海军，航空航天和汽车工业中。自3D弹性层合梁理论（如离散层方法和等效单层模型（ESL））以来，层合复合梁已在许多数学模型中得到了体现。本文介绍了在静态载荷下推导ESL模型基本解和积分方程的数学步骤，称为一阶层压复合梁理论（FOBT）。直接边界元素方法（BEM）解决方案已得到适当解决，其中包含以下主题：（a）影响矩阵的显式形式；（b）集中荷载和（梯形，正弦曲线）分布荷载的荷载矢量；以及（c）简化经典层合梁理论的BEM解。给出了梁在不同静载荷情况，边界条件以及与阶梯梁和连续梁有关的区域不连续性问题的数值结果。结果表明这种直接BEM公式的正确性和有效性。