This study introduces an innovative dynamic infinite meshfree method for robust and efficient solutions to half-space problems. This approach seamlessly couples this method with the nodal integral reproducing kernel particle method to discretize half-spaces defined by an artificial boundary. The infinite meshfree shape function is uniquely constructed using the 1D reproducing kernel shape function combined with the boundary singular kernel method, ensuring the Kronecker delta property on artificial boundaries. Coupled with the wave-transfer function, the proposed approach models dissipation actions effectively. The infinite domain simulation employs the dummy node method, enhanced by Newton–Cotes integrals. To ensure solution stability and convergence, our approach is based on the Galerkin weak form of the domain integral method. To combat the challenges of instability and imprecision, we integrated the stabilized conforming nodal integration method and the naturally stable nodal integration. The proposed methods efficacy is validated through various benchmark problems, with preliminary results showcasing superior precision and stability.

本研究引入了一种创新的动态无限无网格方法，用于稳健且高效地解决半空间问题。该方法将该方法与节点积分再现核粒子方法无缝结合，以离散化由人工边界定义的半空间。采用一维再现核形函数结合边界奇异核方法独特构造无限无网格形函数，保证了人工边界上的克罗内克德尔塔性质。与波传递函数相结合，所提出的方法可以有效地模拟耗散行为。无限域模拟采用虚拟节点方法，并通过牛顿-科特斯积分增强。为了确保解的稳定性和收敛性，我们的方法基于域积分法的伽辽金弱形式。为了应对不稳定和不精确的挑战，我们集成了稳定一致节点积分方法和自然稳定节点积分方法。通过各种基准问题验证了所提出方法的有效性，初步结果显示出卓越的精度和稳定性。