Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dual-support smoothed particle hydrodynamics in solid: variational
  principle and implicit formulation   In this paper, we derive the dual-support smoothed particle hydrodynamics
(DS-SPH) in solid in the framework of variational principle. The tangent
stiffness matrix of SPH is obtained with ease, which can be served as the basis
for implicit SPH. We propose a hourglass energy functional, which allows the
direct derivation of hourglass force and hourglass tangent stiffness matrix.
The dual-support is identified in all derivation 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. Several
numerical examples are presented to validate the method.

30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn