Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The linearized Kirchhoff theory for plates with incompatible prestrain   In this paper, we derive a linearized Kirchhoff model from three dimensional
nonlinear elastic energy of plates with incompatible prestrain as its thickness
$h$ tends to zero and its elastic energy scales like $h^{\beta}$ with
$2<\beta<4.$ The incompatible prestrain is given as a Riemannian metric $G(x')$
in the three dimensional thin plate which only depends on mid-plate of the thin
plates. The problem is studied rigorously by using a variational approach and
establishing the $\Gamma-$ limit of the non-Euclidean version of the nonlinear
elasticity functional when the gauss curvature of the mid-plate $(\Omega,
g=G_{2\times2})$ is always positive, negative or zero.

22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
18
The categories of this paper are: econ