基于映射的高精度混合平面曲梁单元

High Precision Mixed Curved Plane Beam Elements Based on Mapping

通过映射分别实现初始几何和位移场的描述,建立考虑初始曲率和厚度影响的任意平面曲梁的几何关系。采用满足平衡的内力场,提出基于Hellinger-Reissner变分原理的高精度曲梁单元。这种无闭锁新单元可用于具有任意曲率的平面结构,与常规曲梁单元相比,具有更高的精度和效率。算例表明,在模型中准确定义初始几何后,所建立单元可给出极准确的结果。

Through separate mapping of the initial geometry and displacement fields, the geometric relationship of an arbitrarily curved plane beam is established, which includes the effects of variable initial curvature and beam thickness. Using an internal force field satisfying equilibrium conditions, a high precision mixed element is developed for curved beams based on Hellinger-Reissner principle. The proposed new locking-free element can be used to plane structures with arbitrary curvatures. Compared with conventional curved beam elements, the proposed element has much better accuracy and higher efficiency. Numerical examples show that, when the initial geometry is defined in the model, the element can produce extremely accurate results.