A novel implementation of efficient inertia relief analysis using smoothed finite element method for unconstrained structures

TY - JOUR

T1 - A novel implementation of efficient inertia relief analysis using smoothed finite element method for unconstrained structures

AU - Huo, Shuhao

AU - Zhu, Shuai

AU - Liu, Minyang

AU - Bai, Yingchun

AU - Wang, Qiong

AU - Ren, Peng

N1 - Publisher Copyright: © 2026 Elsevier Ltd.

PY - 2026/7

Y1 - 2026/7

N2 - Inertia relief analysis is essential for simulating unconstrained structures subjected to external loads, such as aerospace and automotive systems, where traditional displacement boundary conditions are infeasible. This study systematically integrates the inertia relief technology into the framework of Smooth Finite Element Method (S-FEM). Key contributions include a stabilized S-FEM formulation for inertia relief, and a systematic comparison of computational performance against standard FEM. By smoothing strain fields at element boundaries, S-FEM enhances solution accuracy and mesh adaptability. Approaches for handling inertia relief in cases with and without fictitious constraints are presented, effectively eliminating the rigid-body modes of free-floating systems. Using the mass center of the structure as the reference point, the global acceleration vector is constructed via the rigid-body mode matrix. The consistent mass matrix is adopted instead of the lumped mass matrix to ensure the accuracy of inertial force calculations. The high-performance Pardiso solver is employed to efficiently resolve the resulting symmetric indefinite linear systems, which provides stable and efficient support for solving complex models. Five benchmark cases are utilized to demonstrate the efficiency of the proposed method. Results underscore the framework’s potential for industrial applications requiring rapid analysis of mobile structures without artificial constraints.

AB - Inertia relief analysis is essential for simulating unconstrained structures subjected to external loads, such as aerospace and automotive systems, where traditional displacement boundary conditions are infeasible. This study systematically integrates the inertia relief technology into the framework of Smooth Finite Element Method (S-FEM). Key contributions include a stabilized S-FEM formulation for inertia relief, and a systematic comparison of computational performance against standard FEM. By smoothing strain fields at element boundaries, S-FEM enhances solution accuracy and mesh adaptability. Approaches for handling inertia relief in cases with and without fictitious constraints are presented, effectively eliminating the rigid-body modes of free-floating systems. Using the mass center of the structure as the reference point, the global acceleration vector is constructed via the rigid-body mode matrix. The consistent mass matrix is adopted instead of the lumped mass matrix to ensure the accuracy of inertial force calculations. The high-performance Pardiso solver is employed to efficiently resolve the resulting symmetric indefinite linear systems, which provides stable and efficient support for solving complex models. Five benchmark cases are utilized to demonstrate the efficiency of the proposed method. Results underscore the framework’s potential for industrial applications requiring rapid analysis of mobile structures without artificial constraints.

KW - Computational solid mechanics

KW - Gradient smoothing technique

KW - Inertia relief analysis

KW - Smoothed finite element method

KW - Unconstrained structural systems

UR - https://www.scopus.com/pages/publications/105035669806

U2 - 10.1016/j.enganabound.2026.106770

DO - 10.1016/j.enganabound.2026.106770

M3 - Article

AN - SCOPUS:105035669806

SN - 0955-7997

VL - 188

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

M1 - 106770

ER -