Dual-support smoothed particle hydrodynamics in solid: variational principle and implicit formulation

被引：37

作者：

Ren, Huilong ^{[3
]}

Zhuang, Xiaoying ^{[4
]}

Rabczuk, Timon ^{[1
,2
]}

Zhu, Hehua ^{[4
]}

机构：

[1] Ton Duc Thang Univ, Div Computat Mech, Ho Chi Minh City, Vietnam

[2] Ton Duc Thang Univ, Fac Civil Engn, Ho Chi Minh City, Vietnam

[3] Bauhaus Univ Weimar, Inst Struct Mech, D-99423 Weimar, Germany

[4] Tongji Univ, Coll Civil Engn, State Key Lab Disaster Reduct Civil Engn, Shanghai 200092, Peoples R China

来源：

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2019年 / 108卷

关键词：

Variational principle; Stiffness matrix; Zero-energy mode; Hourglass energy; Implicit formulation; Geometric nonlinearity; Smoothed particle hydrodynamics (SPH); PROPAGATION; SPH; PENETRATION; INTEGRATION; SIMULATION;

D O I：

10.1016/j.enganabound.2019.05.024

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We derive the dual-support smoothed particle hydrodynamics (DS-SPH) in solid within the framework of variational principle. The tangent stiffness matrix of SPH can be obtained with ease, and can be served as the basis for the present implicit SPH. We propose an hourglass energy functional, which allows the direct derivation of hourglass force and hourglass tangent stiffness matrix. The dual-support is involved in all derivations based on variational principles and is automatically satisfied in the assembling of stiffness matrix. The implementation of stiffness matrix comprises with two steps, the nodal assembly based on deformation gradient and global assembly on all nodes. Several numerical examples are presented to validate the method.

引用

页码：15 / 29

页数：15

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