US 11,599,692 B2 · Calculation and analysis method of limit load, deformation and energy dissipating of ring net panel in flexible protection system

Abstract

A calculation method of limit load, deformation and energy dissipating of a ring net panel of a flexible protection net, includes step (1): determining geometrical parameters of the ring net, connection type of steel rings, and diameter of steel wires; step (2): determining a loading rate, a loaded region and a boundary condition of the ring net panel; step (3): obtaining basic mechanical parameters of materials through tests, and establishing a critical damage criterion of the ring net panel; step (4): establishing an equivalent calculation model of a ring net panel based on a fiber-spring unit; and step (5): calculating a puncturing displacement, a puncturing load and energy dissipating of the ring net panel. The method adopts a calculation assumption of load path equivalence.

A method of a quantitative analysis and a design of a reliable flexible protection net by determining a limit load, a deformation, and an energy dissipating of the flexible protection net to meet safety protection requirements, wherein the flexible protection net comprises a ring net panel and a support part, wherein the support part has a protection structure, wherein the ring net panel is connected to the support part through a shackle and a steel rope, and wherein the ring net panel is a nesting of a plurality of single rings, the method comprising:

step (1):
determining geometrical parameters of the ring net panel, the nested net ring, and the steel rope, wherein
an inner diameter of each single ring of the plurality of single rings is d, each single ring is manufactured by winding the steel rope having a diameter of dmin to form different numbers of turns nw, and a cross-sectional area of the single ring it A
A
=
n
w
⁢
π
⁢
d
min
2
4
;
the ring net panel has a length wx and a width wy, a four-nested-into-one ring net panel is formed by using a minimum steel rope having a total length of lwire
l
wire
=
n
w
⁢
π
⁢
d
2
⁢
2
⁢
d
[
(
w
x
-
d
+
2
⁢
2
⁢
d
)
⁢
(
w
y
-
d
+
2
⁢
2
⁢
d
)
+
(
w
x
-
d
)
⁢
(
w
y
-
d
)
]
;
the four-nested-into-one ring net panel is formed by the minimum steel rope having a total mass of mwire;
step (2):
establishing an equivalent calculation model of the ring net panel based on a fiber spring, wherein
a Cartesian coordinate system is selected as a standard coordinate system of the equivalent calculation model, h is a rising height of a loading heading end, a net ring in a loaded region is rectangular after deformation, ax is a side length of the net ring in an x direction, ay is a side length of the net ring in a y direction, and axial deformation of the net ring is ignored, then
{
a
1
+
a
2
=
π
⁢
d
/
2
a
1
/
a
2
=
w
2
/
w
1
⁢

;
the equivalent calculation model presents a biaxial symmetry, the net ring of the loaded region is straightened and intersects with an edge of the loading heading end having a spherical crown shape, a side length of the ring net panel in a positive half axis direction of an axis x is wx, first intersection points at intervals of ax are marked as P1, P2 . . . Pi . . . Pm, and second intersection points at intervals of wx/(2m+1) of a boundary corresponding to the side length of the ring net panel are marked as Q1, Q2 . . . Qi . . . Qm, and at any moment, a coordinate of a point Pi of an edge of the loaded region is:
{
x
P
[
i
]
=
a
x
(
i
-
1
/
2
)
y
P
[
i
]
=
R
p
2
-
a
x
2
(
i
-
1
/
2
)
2
z
P
[
i
]
=
z
⁢
and
⁢
{
x
P
[
i
]
≥
0
y
P
[
i
]
≥
0
z
P
[
i
]
≥
0
;
a coordinate of a point Qi at the boundary is:
{
x
Q
[
i
]
=
w
x
(
i
-
1
/
2
)
/
(
2
⁢
m
x
+
1
)
y
Q
[
i
]
=
w
y
/
2
z
Q
[
i
]
=
0
⁢
and
⁢
{
x
Q
[
i
]
≥
0
y
Q
[
i
]
≥
0
z
Q
[
i
]
≥
0
;
wherein i=1, 2, . . . m, m is an upper limit of i;
a position vector direction of the fiber spring connecting the point Pi and the point Qi is represented as the following equation:
PQ=(xQ[i]−xp[i],yQ[i]−yp[i],−z)
in a loading process, a length value of a ith fiber spring is:
L[i]=|PQ|,L0[i]=|PQ|z=0 ;
wherein L0[i] is an initial length of the ith fiber spring;
at any moment, a fiber length lf and a spring length ls in the ith fiber spring respectively are:
(
a
)
⁢
0
<
γ
N
≤
γ
N
⁢
1
⁢
{
l
s
[
i
]
=
E
f
⁢
1
⁢
A
⁡
(
L
[
i
]
-
l
f
⁢
0
[
i
]
)
+
k
s
⁢
l
s
⁢
0
⁢
l
f
⁢
0
[
i
]
k
s
⁢
l
f
⁢
0
[
i
]
+
E
f
⁢
1
⁢
A
l
f
[
i
]
=
k
s
⁢
l
f
⁢
0
[
i
]
⁢
(
L
[
i
]
-
l
f
⁢
0
)
+
E
f
⁢
1
⁢
Al
f
⁢
0
[
i
]
k
s
⁢
l
f
⁢
0
[
i
]
+
E
f
⁢
1
⁢
A
;
(
b
)
⁢
γ
N
⁢
1
<
γ
N
≤
γ
N
⁢
2
⁢
{
l
s
[
i
]
=
E
f
⁢
2
⁢
A
/
l
f
⁢
0
[
i
]
⁢
(
L
[
i
]
-
l
f
⁢
1
[
i
]
)
+
k
s
⁢
l
s
⁢
1
[
i
]
k
s
+
E
f
⁢
2
⁢
A
/
l
f
⁢
0
[
i
]
l
f
[
i
]
=
k
s
(
L
[
i
]
-
l
s
⁢
1
[
i
]
)
+
l
f
⁢
1
[
i
]
⁢
E
f
⁢
2
⁢
A
/
l
f
⁢
0
[
i
]
k
s
+
E
f
⁢
2
⁢
A
/
l
f
⁢
0
[
i
]
;
wherein lf1 is the fiber length;
ls1 is the spring length when γN=γN1;
γN is a development degree of an axial stress;
γN1 is a development degree of a first axial stress σN1;
and γN2 is a development degree of a second axial stress σN2;
at any moment, an internal force value of the ith fiber spring
F
[
i
]
=
{
K
1
[
i
]
⁢
(
L
[
i
]
-
L
0
[
i
]
)
,
0
<
γ
N
≤
γ
N
⁢
1
K
1
[
i
]
⁢
(
L
1
[
i
]
-
L
0
[
i
]
)
+
K
2
[
i
]
⁢
(
L
[
i
]
-
L
1
[
i
]
)
,
γ
N
⁢
1
<
γ
N
≤
γ
N
⁢
2
;
at any moment, an energy value of the ith fiber spring dissipated in the loading process
E
[
i
]
=
{
K
1
[
i
]
⁢
(
L
[
i
]
-
L
0
[
i
]
)
2
/
2
,
0
<
γ
N
≤
γ
N
⁢
1
K
1
⁢
L
[
i
]
⁢
(
L
1
[
i
]
-
L
0
[
i
]
)
+
K
1
(
L
0
2
[
i
]
-
L
1
2
[
i
]
)
/
2
+
K
2
(
L
[
i
]
-
L
1
[
i
]
)
2
/
2
,
γ
N
⁢
1
<
γ
N
≤
γ
N
⁢
2
;
a length of the ring net panel in a positive half axis of an axis y is marked as wy, third intersection points at intervals of wy/(2n+1) are marked as C1, C2 . . . Cj . . . Cn, fourth intersection points of the boundary corresponding to the length of the ring net panel are marked as D1, D2 . . . Dj . . . Dn;
similarly, coordinates of points Cj and Dj of the edge of the loaded region, a total length L[j] of the jh fiber spring, the internal force value F[j] of the jh fiber spring, and an energy dissipating E[j] at any moment are obtained from symmetry;
step (3):
calculating a puncturing displacement, a puncturing load and the energy dissipating of the ring net, wherein
in a displacement process and the loading process of the ring net panel, when an invalidation occurs in any fiber spring of the equivalent calculation model, the ring net panel is damaged, a damage occurrence condition the ring net panel is:
max
⁢
{
❘
"\[LeftBracketingBar]"
F
[
i
]
❘
"\[RightBracketingBar]"
,
❘
"\[LeftBracketingBar]"
F
[
j
]
❘
"\[RightBracketingBar]"
}
=
γ
N
⁢
max
⁢
σ
y
⁢
n
w
⁢
π
⁢
d
min
2
4
,
and
step (4):
designing the reliable flexible protection net to improve the performance of the net in interception effect using the parameters calculated in previous steps that satisfy safety protection requirements.

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Calculation and analysis method of limit load, deformation and energy dissipating of ring net panel in flexible protection system

Life of this patent

Calculation and analysis method of limit load, deformation and energy dissipating of ring net panel in flexible protection system

Life of this patent

Abstract

Claims19