We consider potential-based interactions between beams (or fibers) and shells (or membranes) using a coarse-grained approach with focus on van der Waals attraction and steric repulsion. The involved 6D integral over volumes of a beam and a shell is split into a 5D analytical pre-integration over the beam's cross section and a surrogate plate tangential to the closest point on the shell, and the remaining 1D numerical integration along the beam's axis. This general inverse-power interaction potential is added to the potential energies of the Bernoulli-Euler beam and the Kirchhoff-Love shell. The total potential energy is spatially discretized using isogeometric finite elements, and the nonlinear weak form of quasi-static equilibrium is solved using the continuation method. We provide error estimates and convergence analysis, together with two intriguing numerical examples. The developed approach provides excellent balance between accuracy and efficiency for small separations.

翻译：本文采用粗粒化方法研究梁（或纤维）与壳（或膜）之间基于势函数的相互作用，重点关注范德华吸引与空间排斥效应。所涉及的梁与壳体积间的六维积分被分解为两部分：首先对梁横截面及壳上最近点处切向替代板进行五维解析预积分，随后沿梁轴线进行剩余的一维数值积分。该通用逆幂次相互作用势被纳入伯努利-欧拉梁与基尔霍夫-洛夫壳的势能体系中。总势能通过等几何有限元进行空间离散化，并采用延拓法求解准静态平衡的非线性弱形式。我们提供了误差估计与收敛性分析，并给出两个具有启发性的数值算例。所发展的方法在微小间距情形下实现了精度与效率的优异平衡。