A new solid-beam approach devoted to thin to very thick beam-like structures is proposed. To meet the beam displacement fields, kinematic relations are directly applied on the solid finite element model which contains several elements through the thickness and width. It is possible to use any beam theory based on kinematic assumptions and three theories are considered in this paper. The classical first-order beam theory, the modified first-order beam theory and a higher-order beam theory lead to the FOSB, the MFOSB and the HOSB models respectively. Linear equations due to kinematic relations are imposed at slave nodes to meet displacement fields throughout the cross-section, resulting in a reduction of the model size. Two examples are presented: a straight beam and a curved beam under distributed loading. The FOSB model gives unsatisfactory results. For a thin beam, the MFOSB model is adequate but leads to moderate errors in the thick case. Compared to the solid model, the HOSB model offers excellent displacements and stresses in thin and thick cases. The final size of these solid-beam models is slightly larger than that of an approach with classical beam elements.

提出了一种新的实体梁方法，专门用于处理薄到非常厚的梁状结构。为了满足梁位移场，运动学关系直接应用于包含多个单元的实体有限元模型，该模型通过厚度和宽度。可以使用基于运动学假设的任何梁理论，本文考虑了三种理论。经典的一阶梁理论、修正的一阶梁理论和高阶梁理论分别导致了FOSB、MFOSB和HOSB模型。由于运动学关系的线性方程被施加在从节点上以满足整个横截面的位移场，从而减小模型尺寸。给出了两个例子：分布载荷下的直梁和弯曲梁。FOSB 模型给出的结果并不令人满意。对于薄梁，MFOSB 模型是足够的，但在厚的情况下会导致中等误差。与实体模型相比，HOSB 模型在薄和厚的情况下提供了出色的位移和应力。这些实体梁模型的最终尺寸略大于经典梁单元方法的尺寸。