A unified quasi-C¹ point interpolation formulation for arbitrary cross-section beams and plates

Guanghui He , Xiaowei Li , Xinkui Li

Abstract

This paper presents a unified quasi-C¹-PIM formulation for high-fidelity static and dynamic analysis of beams and plates with arbitrary cross-sections. The formulation integrates a novel eight-node quadrilateral element that achieves quasi-C¹ continuity through an averaged dual-path interpolation scheme, enabling smooth stress fields without post-processing. Discretizing the cross-section with a quadrilateral mesh and constructing the threedimensional (3D) displacement field reduces the original problem to a one-dimensional (1D) formulation along the structural axis. An adaptive meshfree point interpolation method (PIM) with a tunable support-domain parameter 𝑛0 is employed as the axial solver, facilitating efficient 𝑝-convergence. The proposed method is systematically validated through a series of benchmark problems, including a rocket thrust frame, an L-shaped plate on an elastic foundation, thin-walled beams, composite beams, and frame structures under static and dynamic loading. The results exhibit excellent agreement with high-fidelity 3D finite element models while reducing the system degrees of freedom by 85-95% and achieving up to 3.7× speedup and 61% memory reduction at comparable accuracy levels. Parametric studies confirm stable convergence with respect to cross-sectional mesh refinement, axial node density, and the support-domain parameter. By combining geometric generality, inherent stress smoothness, and computational efficiency, the quasi-C¹-PIM framework provides a unified and reliable 1D numerical approach for analyzing complex beam and plate structures.

Key Words

arbitrary cross-section beams; dimensional reduction; point interpolation method; quasi-C¹ continuity; smooth stress analysis; unified beam-plate formulation

Address

Guanghui He — School of Intelligent Construction, Shanghai Technology and Innovation Vocational College, 925 North Renmin Road, Shanghai, 201620, China; Shanghai Songjiang Industry-Education Integration Research Center, Shanghai Open University, 288 Guoshun Road, Shanghai, 200433, China; Central Research Institute of Shanghai Construction Group, Shanghai Construction Group, 700 Xinjunhuan Road, Shanghai, 201114, China
Xiaowei Li — School of Intelligent Construction, Shanghai Technology and Innovation Vocational College, 925 North Renmin Road, Shanghai, 201620, China; Shanghai Songjiang Industry-Education Integration Research Center, Shanghai Open University, 288 Guoshun Road, Shanghai, 200433, China
Xinkui Li — Central Research Institute of Shanghai Construction Group, Shanghai Construction Group, 700 Xinjunhuan Road, Shanghai, 201114, China

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