Construction of a Model of Interaction of a Fiber-reinforced Plate
with an Elastic Base
А. N. Pestryakov
1
, I. G. Ovchinnikov
1,2
and A. S. Demidov
1
1
Ural State University of Railway Transport, Yekaterinburg, Russia
2
Saratov State Technical University Named After Yuri Gagarin, Saratov, Russia
Keywords: fiber-reinforced concrete, fiber concrete, elastic base plate, rigid pavement, modeling of fiber concrete,
approximation of experimental data.
Abstract: The article considers a special case of calculation of thin-walled structures, namely plates on an elastic base,
as a structure with a fairly significant scope of application in transport construction. The issues related to the
construction of a model of deformation of fiber-reinforced plates with an elastic base are considered. In the
context of solving the above-mentioned issues, an analysis of the deformation diagrams of fiber-reinforced
concrete (fiber concrete), as well as physically nonlinear relations describing the deformations of fiber-
reinforced material that variously resists tensile and compression deformations under the plane stress state
characteristic of plates, is given.
1 INTRODUCTION
After the beginning of the economic crisis in 2008,
transport builders faced a very important problem of
reducing the strength of building materials while
maintaining their strength properties. Constant
changes in prices for materials and labor costs
forced Gosstroy to abandon the basic index pricing
method (the main method in force since 1991) in
2016 and switch to the resource method. This
method has fully justified itself during the crisis
caused by sanctions and the coronavirus pandemic
(COVID-19). Designers began to regularly,
according to Customer requirements, in order to
reduce the cost, recalculate the ratio of concrete-
reinforcement in building structures (Kokodeev,
2020).
One of the important scientific directions was the
development of new materials with predetermined
properties, as well as the study of the stress-strain
state (SSS) of structures made of them (Varakin,
2020). In the manufacture of thin-walled structures
of transport structures, the use of fiber-reinforced
concrete (fiber concrete), which has significantly
greater resistance to the appearance and growth of
cracks compared to conventional concrete, proved to
be very effective. This article considers a special
case of thin-walled structures, namely plates on an
elastic base, as a structure with a fairly significant
scope of application in transport construction. This
is a scientific problem, the solution of which has
great practical potential.
Within the framework of solving this problem,
the article presents an analysis of the state of the
issue, the construction of a model of deformation of
fiber-reinforced plates on an elastic base, and also
provides a method for calculating such structures.
The solution of the problem is reduced to the
consideration of such tasks:
1. Analysis of the mechanical properties of fiber-
reinforced concrete under various stress conditions.
2. Construction of a model of deformation of
fiber-reinforced concrete as a non-linearly
deformable material sensitive to the type of stress-
strain state.
3. Development of a method for calculating
fiber-reinforced plates on an elastic base, which
allows analyzing their stress-strain states under
different boundary conditions and loading programs.
2 MATERIALS AND METHODS
A large number of researchers have been engaged in
increasing the rigidity and crack resistance of
structures. One of the promising directions is the use
Pestryakov, A., Ovchinnikov, I. and Demidov, A.
Construction of a Model of Interaction of a Fiber-reinforced Plate with an Elastic Base.
DOI: 10.5220/0011581400003527
In Proceedings of the 1st International Scientific and Practical Conference on Transport: Logistics, Construction, Maintenance, Management (TLC2M 2022), pages 187-195
ISBN: 978-989-758-606-4
Copyright
c
 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)
187

of composites (materials that are heterogeneous in
their composition). Usually, researchers consider
polystructural composites, i.e. systems composed of
many structures (Selyaev, 1993; 2. Selyaev, 1986).
The mechanical characteristics of fiber
reinforcement are usually much higher than the
mechanical characteristics (Skudra, 1975).
When creating thin-walled structures of transport
structures, composite material from a concrete
matrix and reinforcing elements should be used, as
which either fibers in the form of separate rods, or
fine-mesh grids, or sections of steel fibers are used
(Kurbatov, 1980; Kurbatov, 1980). These randomly
arranged fibers lead to a significant increase in crack
resistance, and also improve the resistance of the
composite to the action of tensile stresses. Quite a
lot of works and publications have been devoted to
the study of various issues of the behavior of fiber-
reinforced concrete, and, as follows from (Nekrasov,
1925), these issues were investigated by Professor
V.P. Nekrasov at the beginning of the XX century.
Over the past three decades, extensive studies
have been conducted on the mechanical
characteristics of concrete, dispersed reinforced with
both steel and synthetic fiber. Professor Stepanova
D.S. (Stepanova, 1975), studying fiber concrete,
determines the dispersion of the fiber filler (the
degree of crushing and dispersal of reinforcement in
the structure) through the ratio between the total
surface of the fiber reinforcement and the volume of
reinforced concrete. And in the work of Tsiskreli
G.D. (Tsiskreli, 1954), dispersion refers to the ratio
between the percentage of fiber reinforcement and
the diameter of fiber reinforcement. Moreover,
despite the differences in the terminology used, it
was concluded that with an increase in the
dispersion index, the work of fiber-reinforced
concrete under tension improves, which delays the
appearance of cracks.
It is possible to note different directions of
research on the work of fiber-reinforced structures:
− study of the adhesion of the filler to concrete
depending on its saturation with fibers, (works
by Kravinskis V.K., Vylegzhanin V.P.
(Vylegzhanin, 1982; Kravinskis, 1979));
− study of structural characteristics of steel fiber
concrete, (works of Kopatsky A.V., Lobanov
I.A. (Lobanov, 1976; Kopatsky, 1979));
− study of the dependence of the parameters of
fiber reinforcement and the properties of the
concrete matrix, as well as the selection of the
optimal composition of the steel-fiber concrete
mixture according to certain parameters
(works by Polyakova L.G., Ovchinnikov I.G.,
Rabinovich F.N. (Ovchinnikov, 1990;
Rabinovich, 1985));
− study of the location of reinforcing fibers on
the properties of fiber-reinforced concrete)
works by Browns Ya.A., Nagevich Yu.M.,
Lagutina G.E., Lavrinev P.G. (Browns, 1986;
Lavrinev, 1983; Rodov, 1980)).
Obviously, this is not a complete list of modern
research directions for such materials and structures
made of them. At the moment, it has been revealed
that the presence of fiber slows down the crack
opening process from 6 to 20 times, depending on
the reinforcement parameters, the loading level
compared to traditional reinforced concrete (with the
same percentage of reinforcement) (Grigoriev, 1983;
Kadysh, 1982; Kurbatov, 1982; Pavlov, 1976;
Varakin, 2020).
This leads to the conclusion about the
effectiveness of using a composite based on a
concrete matrix and steel fiber in the manufacture of
thin-walled structures of transport structures (it is
characteristic that with thick-walled structures, the
advantages of fiber reinforcement are leveled).
In transport construction, flexible pavement has
been widely used for quite a long time, which,
unfortunately, have a short service life in severe
operating conditions. In Russia, many regions are
characterized by a sharply continental climate. It is
characterized by the freezing of soils to a
considerable depth, the presence of permafrost
zones. In this case, rigid structures of pavement
provide long service life. Building structures in the
form of thin-walled plates have become widespread
in various industries. Walls of premises, road
pavement, airfield coverings, regulatory structures
made according to the scheme of rigid plates and
slabs are widely used in modern construction.
In transport construction, plates are used as a
coating on highways with high traffic intensity, with
embankments of poor soils, on urban roads, in areas
where heavy machinery is used, as a coating of
runways at airfields, etc. Road pavement in the form
of plates of fiber-reinforced concrete has a number
of significant advantages compared to flexible
pavement:
− changes in external temperature influences
practically do not affect the stability of
mechanical properties;
−
the use of such coatings provides a longer
service life before major repairs;
− with increasing age of fiber-reinforced
concrete, its strength increases;
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188

− the strength and rigidity of fiber-reinforced
concrete is significantly greater than that of
asphalt concrete;
− stability and its weak dependence on the
humidity of the coefficient of adhesion of
coatings made of fiber-reinforced concrete
with a car wheel.
The above data suggest that the scheme of
operation of rigid pavement can be attributed to the
operation of plates on an elastic base.
In recent years, a composite based on steel fiber
concrete has often been used for reinforced concrete
coatings. Composite (composite material) is an
artificial material obtained by a volumetric
combination of different components performing
various functions. One component (matrix) is
responsible for plasticity and elasticity, the other
(filler) for strength and rigidity. At the same time,
the final system has a pronounced emergence (that
is, the properties of the composite differ from the
properties of the constituent components). In this
case, the composite material is continuous and the
forces transmitted to it are distributed continuously
over its volume.
When constructing a model of deformation of
fiber-reinforced plate on an elastic base, we will rely
on standard hypotheses, according to which the
layers of the plate do not press on each other and the
hypothesis of direct normals is valid.
Cut out a rectangular element from the plate a
bcd with infinitesimally small dimensions dx, dy
(Fig. 1) on which a load of intensity q normal to the
surface acts from above, and an elastic base reaction
of intensity p acts from below. On the face cd act
forces
x
Q
and S
у,
, tensile force N
x
, bending and
torques М
x
and H. In turn, on the face ab, which is
separated from c d by an infinitesimal distance dx,
the above forces and moments differ by infinitesimal
quantities
dx
x
Q
x
∂
∂
,
dx
x
S
у
∂
∂
,
dx
x
N
x
∂
∂
,
dx
x
M
x
∂
∂
,
dx
x
H
∂
∂
.
Similarly, it is possible to obtain both forces and
moments on the faces a d and bc.
The equilibrium of this infinitesimal element will
be ensured when the conditions of equilibrium of the
projections of all forces on the coordinate axis and
the equilibrium of bending and torques relative to
the axes are met.
Figure 1: Forces acting on an infinitesimal element.
The projection of all efforts on the Z axis will be
recorded (1):
0
y
x
xxy
y
Q
Q
QdxdyQdyQdydx
xy
Q dx pdxdy
∂

∂

+−++−


∂∂


+=
. (1)
Giving similar terms, we get (2):
p
y
Q
x
Q
y
x
−=
∂
∂
+
∂
∂
(2)
The condition of equilibrium of bending and
torques relative to the X axis will be written (3):
2
2
2
()
()
2
()
2
() 0
2
y
yy
x
x
x
y
y
M
MdydxMdx
y
Hdy
HdxdyHdyQ
x
Q
dy
Qdx
x
Q
dy
Q dy dxdy pdx
y
∂
+−+
∂
∂
+−+−
∂
∂
−+ −
∂
∂
+−=
∂
(3)
Giving such terms and neglecting the small-order
magnitude
0
2
→
∂
∂
dy
y
Q
y
, we write (4):
y
y
Q
x
H
y
M
=
∂
∂
+
∂
∂
(4)
The condition of equilibrium of bending and
torques relative to the Y axis will be written (5):
x
x
Q
y
H
x
M
=
∂
∂
+
∂
∂
(5)
Construction of a Model of Interaction of a Fiber-reinforced Plate with an Elastic Base
189

As a result of the transformation of the above
formulas , we obtain the following equilibrium
equation (6):
2
22
22
2
y
x
M
MH
p
xxyy
∂
∂∂
++=−
∂∂∂∂
(6)
Analysis of experimental results obtained in the
study of the mechanical properties of fiber-
reinforced concrete with sufficient justification
suggests that the behavior of fiber-reinforced
concrete can be described using a model of
orthotropic nonlinear multi-resistive material.
In the case of a flat stress state in which a plate
of fiber-reinforced concrete is located, the physical
relations for an orthotropic nonlinear resistive
material take the form (7):
j
xy
xy
xi
xi
x
yj
y
y
yj
yj
y
xi
x
x
G
e
e
e
τ
ν
ψ
σ
ψ
σ
ν
ψ
σ
ψ
σ
=
−=
−=
(7)
where
e;;
τ
σ
components of the stress
tensor and strain tensor,
ν
- Poisson's ratio, x, y –
coordinates, i and j –take into account the direction
of deformation, and (i(j)=1 -stretching, i(j)=2 -
compression), G
j
- shear modulus,
ψ
- nonlinear
functions that take into account the nonlinearity of
the deformation diagram and the resistance of fiber-
reinforced concrete (8):
u
uyj
yj
u
uxi
xi
e
e
e
e
)(
;
)(
φ
ψ
φ
ψ
=
=
(8)
here
u
e
is the intensity of deformations,
yjxi
φ
φ
;
which quite correctly describe the
deformation diagrams of fiber-reinforced concrete,
taking into account the direction and type of
deformation (9):
yjyj
xixi
m
uyj
k
uyjyj
m
uxi
k
uxixi
eBeA
eBeA
−=
−=
φ
φ
;
(9)
coefficients A
xi
, In
yj
, k
xi
, m
yj
are located in such
a way as to provide the best approximation of the
deformation diagrams of fiber-reinforced concrete.
The shift modulus G
j
- is defined through these
functions
yjxi
ψ
ψ
,
and quantities
yjxi
ν
ν
,
by the
following expression (10):








−
+
−
+
= ))(
1
1
(2
1
yx
x
yj
yj
xi
xi
j
G σσ
σ
ψ
ν
ψ
ν
( 1 0 )
Finding from the physical relations of the
voltage, we can write (11):
xyjxy
xiy
ji
j
y
yjx
ji
i
x
eG
ee
ee
=
+
−
=
+
−
=
τ
ν
νν
ψ
σ
ν
νν
ψ
σ
)(
1
)(
1
(11)
The experimental deformation diagram of fiber-
reinforced concrete is approximated by the function
(12):
3
11
3
22
0
0
AB for
AB for
εε σ
σ
εε σ

−≥

=

−<


(12)
The coefficients of which can be easily
determined from the conditions of the minimum
functional (13)
min)(
n
1j
3
→−−=

=
экс
jjj
BAI σεε
(13)
As a result, we get the following expressions for
finding them (14):
2
1
4
1
6
1
2
1
4
1
3
1
6
1








−
































−
















=


===
====
n
j
j
n
j
j
n
j
j
n
j
j
n
j
jj
n
j
j
n
j
jj
A
εεε
εεσεεσ
2
1
4
1
6
1
2
1
2
1
3
1
4
1








−
































−
















=


===
====
n
j
j
n
j
j
n
j
j
n
j
j
n
j
jj
n
j
j
n
j
jj
B
εεε
εεσεεσ
(14)
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Indexes at coefficients A and B are omitted.
Note that the values of the coefficients A
1
, B
1
are based on experimental strain curves under
tension, and the coefficients A
2
, B
2
are based on
experimental data under compression.
If we do not take into account the nonlinearity of
deformation of fiber-reinforced concrete, but take
into account only its resistance to deformation, then
the deformation diagram can be described by the
function (15):
иiии
Eс εεσ =),(
(15)
where i=1 corresponds to stretching, and i=2
corresponds to compression.
To assess the suitability of the above relations for
describing the deformation of fiber concrete, we use
the experimental data shown in Fig. 2
In this case, to determine the elastic modulus E,
we use the minimum condition of the following
functional (16).
min)(
n
1j
2
→−=

=
i
э
i
ЕI εσ (16)
As a result, we get the expression (17):
1
2
1
.
n
ii
i
n
i
i
E
σε
ε
=
=
=


(17)
The results of the description of the deformation
curves of fiber concrete and fiber concrete with the
addition of CMID according to various models are
given in Table 1 and 2. The deviation of theoretical
data from experimental data is also shown there.
As can be seen, when using a nonlinear
deformation model to describe experimental results,
the results mostly fall into a five percent error
corridor. When using a linear model, the
approximation error reaches 15-20%.
Let's make up the resolving equation of a plate of
fiber-reinforced concrete on an elastic base.
Expressions for moments and efforts will be taken in
the following form (18):

∂+∂=
−
2
2
h
z
фб
xi
z
h
фб
xj
фб
х
x
x
zzzzМ σσ
,

∂+∂=
−
2
2
h
z
фб
yi
z
h
фб
yj
фб
y
y
y
zzzzМ σσ
,

∂+∂=
−
2
2
h
z
ôá
xyi
z
h
ôá
xyj
ôá
xy
xy
zzzzH ττ
,

∂+∂=
−
2
2
h
z
фб
xi
z
h
фб
xj
фб
х
x
x
zzN σσ
,

∂+∂=
−
2
2
h
z
фб
yi
z
h
фб
yj
фб
y
x
x
zzN σσ
,

∂+∂=
−
2
2
h
z
фб
xyi
z
h
фб
xyj
фб
xy
xy
zzS ττ
, (18)
Figure 2: Dependenceε from σ(under compression) for a- concrete and fiber concrete, b-for concrete and fiber concrete with
the addition of CMID-4 (Pestryakov, 2003; Polyakova, 1991).
Construction of a Model of Interaction of a Fiber-reinforced Plate with an Elastic Base
191

Table 1: The results of modeling experimental deformation curves of fiber concrete with the addition of CMID under
compression, and: A
2
=36.44* 10
3
Mpa, B
2
=46.20* 10
8
Mpa, E
2
=28.93* 10
3
Mpa.
Experimental
values of
stresses, MPa
Experimental
values of
deformations,
mm
Calculated
stresses
according to
the nonlinear
model. MPa
Calculated
stresses
according to
the linear
model. MPa
Deviations in
the nonlinear
model, MPa
Deviations in
the linear
model, MPa
Error of the
nonlinear
model %
Error of the
linear model
%
4,00 0,00011 4,16 3,30 0,16 -0,70 3,90 -17,38
8,00 0,00021 7,76 6,20 -0,24 -1,80 -3,00 -22,54
12,00 0,00032 11,55 9,30 -0,45 -2,70 -3,71 -22,54
16,00 0,00043 15,25 12,39 -0,75 -3,61 -4,70 -22,54
20,00 0,00055 19,38 16,01 -0,62 -3,99 -3,09 -19,96
24,00 0,00070 23,81 20,14 -0,19 -3,86 -0,80 -16,08
28,00 0,00085 28,03 24,48 0,03 -3,52 0,12 -12,58
32,00 0,00104 32,60 29,95 0,60 -2,05 1,87 -6,40
36,00 0,00129 37,02 37,18 1,02 1,18 2,85 3,28
40,00 0,00162 39,39 46,99 -0,61 6,99 -1,53 17,48
Table 2: The results of modeling experimental deformation curves of fiber concrete with the addition of CMID under
tension, and: A
1
=30.71* 10
3
Mpa, B
1
=11.79* 10
10
Mpa, E
1
=22.21* 10
3
Mpa.
Experimental
values of
stresses, MPa
Experimental
values of
deformations,
mm
Calculated
stresses
according to
the nonlinear
model. MPa
Calculated
stresses
according to
the linear
model. MPa
Deviations in
the nonlinear
model, MPa
Deviations in
the linear
model, MPa
Error of the
nonlinear
model %
Error of the
linear model
%
1,00 0,00003 0,98 0,71 -0,02 -0,29 -1,71 -28,65
2,00 0,00005 1,52 1,11 -0,48 -0,89 -23,99 -44,50
3,00 0,00010 3,05 2,30 0,05 -0,70 1,62 -23,36
4,00 0,00014 3,96 3,09 -0,04 -0,91 -1,06 -22,70
5,00 0,00020 5,20 4,44 0,20 -0,56 3,95 -11,21
6,00 0,00032 5,96 7,14 -0,04 1,14 -0,73 18,92
Here z
x
(x,y), z
y
(x,y), z
xy
(x,y) are functions
describing the position of neutral surfaces
determined from the conditions
σ
x
=0, σ
y
=0,
xyj
τ
=0
and separating the stretched zones of the fiber-
reinforced plate from the compressed ones, and if
the lower zone of the bent plate is stretched, then j
=1, i=2, if the upper zone is stretched and the lower
one is compressed, then j=2, i=1. The functions z
x
(x,y), z
y
(x,y), z
xy
(x,y) are expressed in terms of
deformation parameters as follows (19):
yix
yix
x
z
χνχ
ε
ν
ε
+
+
−=y)(x,
;
xjy
xjy
y
z
χνχ
ε
ν
ε
+
+
−=y)(x,
; (19)
xy
xy
xy
z
χ
ε
2
y)(x, −=
If you use the notation (20):
ji
i
i
νν
ψ
α
−
=
1
,
ji
j
j
νν
ψ
α
−
=
1
,








−
+
−
+
= ))(
1
1
(2
1
yx
x
yj
yj
xi
xi
j
σσ
σ
ψ
ν
ψ
ν
β








−
+
−
+
= ))(
1
1
(2
1
xy
y
xi
xi
yj
yj
i
σσ
σ
ψ
ν
ψ
ν
β
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192


∂+∂=
−
2
2
h
z
k
i
z
h
k
j
х
k
х
х
zzzzJ αα
, for k=0,1,2

∂+∂=
−
2
2
h
z
k
i
z
h
k
j
y
k
y
y
zzzzJ αα
, at k=0,1,2 (20)

∂+∂=
−
2
2
h
z
k
ii
z
h
k
jj
x
k
x
x
zzzzI νανα
, at k=0,1,2

∂+∂=
−
2
2
h
z
k
ii
z
h
k
jj
y
k
y
y
zzzzI νανα
, at k=0,1,2

∂+∂=
−
2
2
h
z
k
i
z
h
k
jk
xy
xy
zzGzzGT
, at k=0,1,2
Then the bending and torques, as well as the
forces, can be written as (21):
x
y
x
y
x
x
x
x
фб
x
IIJJM
2121
χεχε +++=
;
y
x
y
x
y
y
y
y
фб
y
IIJJM
2121
χεχε +++=
фб
xy
фб
xy
фб
TTH
21
2 χε +=
;
x
y
x
y
x
x
x
x
фб
x
IIJJN
1010
χεχε +++=
(21)
y
x
y
x
y
y
y
y
фб
y
IIJJN
1010
χεχε +++=
;
фб
xy
фб
xy
фб
TTS
10
2 χε +=
If there are no linear normal and horizontal shear
forces in the plate sections N
x
=0, N
y
=0, S=0, then
using additional convolution notation (22):
yxyx
xyyx
IIJJ
JJII
f
1010
1010
2
−
−
=
;
yxyx
yxyx
IIJJ
JIJI
f
1010
1010
1
−
−
=
,
yxyx
xyxy
IIJJ
JJII
f
1010
0110
4
−
−
=
yxyx
xyxy
IIJJ
JIJI
f
1010
0110
3
−
−
=
, (22)
we can find fairly simple expressions for
deformations
ε
x
, ε
y
, ε
xy
(23):
yxx
ff χχε
12
+=
,
yxy
ff χχε
43
+=
,
xyxy
T
T
χε








−=
0
1
2
(23)
Considering additional notations (24):
xxx
JIfJfD
213121
++=
;
yxx
IIfJfD
214112
++=
;
yyy
IIfJfD
212133
++=
;
yyy
JIfJfD
211144
++=
; (24)
0
2
1
25
)(
22
T
T
TD −=
,
we get (25):
yxx
DDM χχ
21
+=
,
yxy
DDM χχ
43
+=
,
xy
DH χ
5
=
(25)
Using the expressions for bending and torques M
x
, M
y
, H, we transform the initial equilibrium
equation into the differential equation of bending of
a plate made of fiber-reinforced concrete interacting
with an elastic base (26):
22 2 2
12
222 2
2222
53
22
22
4
22
2
(, ) (, )
ww
DD
xxxy
ww
DD
xy xy y x
w
Dpx
y
qx
y
yy

∂∂ ∂∂
++

∂∂∂∂


∂∂∂∂
++

∂∂ ∂∂ ∂ ∂


∂∂
+=−

∂∂

(26)
3 RESULTS AND DISCUSSION
In the article, models of deformation of an
orthotropic nonlinear multi-modulus fiber-reinforced
structure under the conditions of a plane stress state
characteristic of bent plates are constructed. As a
result of the identification of models of deformation
of the material using experimental data on the
stretching and compression of fiber concrete, the
coefficients of the models were determined. Using
the proposed nonlinear orthotropic multi-resistive
model of deformation of fiber-reinforced concrete,
differential equations are obtained that are a model
of deformation of a plate of fiber-reinforced concrete
interacting with an elastic base. This model
describes the deformation of a fiber-reinforced plate
on an elastic base under various boundary conditions
on the contour. The work of the elastic base can be
taken into account according to one or another
Construction of a Model of Interaction of a Fiber-reinforced Plate with an Elastic Base
193

model by specifying an expression for the rebuff of
the elastic base p .
4 CONCLUSIONS
A fairly wide range of scientific methods were used
in the work. Experimental data were collected and
analyzed, mathematical modeling was performed,
and numerical simulation results were compared
with experimental data. It is shown that the
nonlinear multi-modulus model of fiber concrete
deformation shows a much better approximation of
experimental data than the linear, albeit multi-
modulus model. All this in general allowed us to
draw a conclusion about the reliability of the results.
The practical significance of the article consists in
constructing models of deformation of a fiber-
reinforced plate interacting with an elastic base,
taking into account the nonlinearity and diversity of
the plate material. The results of the work are used
in the educational process in the training of civil
engineers when presenting the issues of calculating
structures interacting with an elastic base, taking
into account the real conditions of the properties of
fiber-reinforced concrete from which the structures
are made. It should also be noted that the obtained
model of deformation of a fiber-reinforced concrete
plate operating on an elastic base can be effectively
used in the calculation of roadway plates on bridge
structures, in the calculation of rigid road pavement
made of fiber-reinforced concrete arranged on
highways.
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195