3. Modeling A#

3.1. Characteristics of modeling#

It is a modeling in plane constraints.

Y, V

X, U

Decoupage: \(4\mathrm{\times }4\) elements

Boundary conditions:

in \(O\), \(u\mathrm{=}v\mathrm{=}0\)
in \(B\), \(u\mathrm{=}0\)

3.2. Characteristics of the mesh#

Number of knots: 65

Number of meshes and type: 16 QUAD8

Node name

\(O=\mathrm{N38}\)

\(A=\mathrm{N1}\)

\(B\mathrm{=}\mathit{N23}\)

\(C=\mathrm{N16}\)

\(D=\mathrm{N3}\)

\(\mathrm{B1}=\mathrm{N9}\)

\(\mathrm{C1}=\mathrm{N30}\)

3.3. Tested sizes and results#

Location	Value type	Reference
Point \(A\)	\(T\)
Point \(B\)	\(T\)
Point \(C\)	\(T\)
Point \(D\)	\(T\)
Point \(\mathrm{B1}\)	\(T\)
Point \(\mathrm{C1}\)	\(T\)
Point \(O\)	\(T\)
Point \(A\)	\(u\)	2.68975
	\(v\)	2.55
Point \(B\)	\(u\)
	\(v\)	-2.65125
Point \(C\)	\(u\)	-2.695
Point \(D\)	\(u\)	-2.7002
	\(v\)	-2.695
Point \(\mathrm{B1}\)	\(u\)	0.0700
	\(v\)	2.59875
Point \(\mathrm{C1}\)	\(u\)	2.625

3.4. notes#

It is necessary to finely discretize function \(E(t)\) in order to obtain satisfactory results. For this test, 160 discretization points were taken, for the temperature range [5., 75.].