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math.NA2026

Nonlinear Geotechnical Analysis Using a Polygonal Cell-Based Smoothed Finite Element Framework

Mingjiao Yan, Yang Yang, Zongliang Zhang +6

Nonlinear geotechnical analysis often involves complex geometries, staged construction, local failure, and mesh-dependent stress and plastic strain responses. This study develops a…

math.NA2026

Two-dimensional seepage analysis using a polygonal cell-based smoothed finite element method

Yang Yang, Mingjiao Yan, Zongliang Zhang +3

This study develops a polygonal cell-based smoothed finite element method (CSFEM) for two-dimensional seepage analyses in porous media, covering steady-state, transient, and free-s…

math.NA2025

Elasto-plastic cell-based smoothed finite element method solving geotechnical problems

Yang Yang, Mingjiao Yan, Zongliang Zhang +4

This work develops an elasto-plastic cell-based smoothed finite element method (CSFEM) for geotechnical analysis. The formulation incorporates a smoothed strain field into the stan…

math.NA2025

Three dimensional seepage analysis using a polyhedral scaled boundary finite element method

Mingjiao Yan, Yang Yang, Zongliang Zhang +3

This work presents a polyhedral scaled boundary finite element method (PSBFEM) for three dimensional seepage analysis. We first derive the scaled boundary formulation for 3D seepag…

math.NA2025

Steady-state and transient thermal stress analysis using a polygonal finite element method

Yang Yang, Mingjiao Yan, Zongliang Zhang +3

This work develops a polygonal finite element method (PFEM) for the analysis of steady-state and transient thermal stresses in two dimensional continua. The method employs Wachspre…

math.NA2025

A polyhedral scaled boundary finite element method solving three-dimensional heat conduction problems

Mingjiao Yan, Yang Yang, Chao Su +4

In this study, we derived a three-dimensional scaled boundary finite element formulation for heat conduction problems. By incorporating Wachspress shape functions, a polyhedral sca…