Background. In recent years, there has been a rapid development of the domestic military industry. Reducing the mass and increasing the specific strength of military products used in the field – the ...most pressing challenges facing engineers and scientists today. The rapid development of adaptive production has significantly expanded the possibilities of methods of topological optimization in the design of new products or improvement of existing design and technological solutions in order to reduce weight.
Objective. The purpose of the paper is to improve the efficiency of designing the technology of manufacturing a frame type construction based on the method of topological optimization, which will reduce the weight of the product, while maintaining all the specified functional parameters.
Methods. The paper presents an analysis of topological optimization methods and offers the interaction of modern ADS, namely CAD, CAM, CAE modules at the stage of design and technological preparation of production, which once again demonstrated its effectiveness in solving problems to reduce product weight.
Results. The main tasks of topological optimization were solved for the frame type constructions, such as the minimization of volume and mass under physical constraints, as well as the optimization of other parameters with given geometric constraints. As a result, the proposed method of reducing the weight of the product is improved, which due to rational design and technological measures ensured a 56 % reduction in the weight of the frame type structure from the original and reduced the complexity of the manufacturing process by 22 % due to its effective adaptation to new technological conditions.
Conclusions. The application of methods of topological optimization and rational establishment of design and technological constraints on products at the design stage can be very effective in solving problems of reducing the weight of products and optimizing manufacturing processes.
The paper deals with modification and minor correction of the presentation and results of paper (http://dx.doi.org/10.1016/j.apm.2015.09.103). The current paper demonstrates that the solution ...obtained in the paper (doi.org/10.1016/j.apm.2015.09.103) for the thin cylindrical shell problem holds well near the cylindrical edge surfaces but may deviate near the mid-cylindrical surface. The reason behind it, is the observation of the paper (doi.org/10.1016/j.apm.2015.09.103) that different asymptotic modes are uncoupled, can be justified near edge surfaces but not near the mid-surface. In this paper an attempt is made to predict the vibration near mid-surface of the shell with a prior knowledge of the solution near edge surfaces, which has already been discussed in (doi.org/10.1016/j.apm.2015.09.103).
This study presents a distortion-gradient model for an isotropic plastically deformed solid within the framework of finite deformation theory. The work aims to provide an alternative form of the ...Gurtin and Anand (Int J Plast 21:2297–2318,
2005
) finite deformation strain-gradient model with a view to relaxing the constraint of irrotationality of plastic flow. The kinematic gradient of deformation is assumed to admit the Kroner–Lee decomposition into elastic and plastic parts. The obtained microforce balance, constitutive relations and plastic flow rule are similar to that obtained by Gurtin and Anand but different in that the present theory used a codirectionality hypothesis to obtain thermodynamically consistent constitutive relations for the dissipative microstresses.
The paper considers elastic stress distributions in infinite space with hyperbolic notch when normal or tangential stresses are given on the boundary of notch. The work considers plane deformation. ...So, exact (analytical) solution of two-dimensional boundary value problems of elasticity in the domain with hyperbolic boundary in the elliptic coordinate system is constructed using the method of separation of variables. The stress–strain state of a homogeneous isotropic infinite body with a hyperbolic cut is studied when there are non-homogeneous (nonzero) boundary conditions given on the hyperbolic cut. Finally, the numerical simulation is performed to the stress and displacement distributions over a finite size volume surrounding the notch and relevant graphs for the numerical results of some test problems are presented.
The paper is concerned with methodological and experimental verification of multimodulus linear elasticity model for an isotropic body during tension and compression tests of solid samples of ...different origin and structure. We analyze the reasons why the values of Young’s modulus recorded during tension–compression tests are different. It is shown that using appropriate test techniques and equipment for measuring and recording deformations in a homogeneous uniaxial stress state makes it possible to obtain statistically insignificant differences in Young’s modulus for a number of materials subjected to tensile and compressive loads.
Let
K be an isotropic convex body in
R
n
and let
Z
q
(
K
)
be the
L
q
-centroid body of
K. For every
N
>
n
consider the random polytope
K
N
:
=
conv
{
x
1
,
…
,
x
N
}
where
x
1
,
…
,
x
N
are ...independent random points, uniformly distributed in
K. We prove that a random
K
N
is “asymptotically equivalent” to
Z
ln
(
N
/
n
)
(
K
)
in the following sense: there exist absolute constants
ρ
1
,
ρ
2
>
0
such that, for all
β
∈
(
0
,
1
2
and all
N
⩾
N
(
n
,
β
)
, one has:
(i)
K
N
⊇
c
(
β
)
Z
q
(
K
)
for every
q
⩽
ρ
1
ln
(
N
/
n
)
, with probability greater than
1
−
c
1
exp
(
−
c
2
N
1
−
β
n
β
)
.
(ii)
For every
q
⩾
ρ
2
ln
(
N
/
n
)
, the expected mean width
E
w
(
K
N
)
of
K
N
is bounded by
c
3
w
(
Z
q
(
K
)
)
.
As an application we show that the volume radius
|
K
N
|
1
/
n
of a random
K
N
satisfies the bounds
c
4
ln
(
2
N
/
n
)
n
⩽
|
K
N
|
1
/
n
⩽
c
5
L
K
ln
(
2
N
/
n
)
n
for all
N
⩽
exp
(
n
)
.
•Vibration of a thin cylindrical shell problem is formulated.•Formulation is done by asymptotic approach under cylindrical symmetry.•Analytical solutions are obtained with clarity.•Obtained solutions ...are numerically discussed.
In this paper, a dynamic behavior of an isotropic cylindrical shell under cylindrical symmetry is presented by asymptotic approach. Here some special assumptions are set to make the problem simple. An attempt is taken to give an analytic expression of radial vibration of a semi-infinite cylinder. In this problem it is assumed that the thickness of the shell is so small that variants of the vibrations exhibit infinite power series expansion across the thickness. As a result of this assumption it is shown that all modes of variants remain uncoupled and satisfy the same equations of motion approximately.
This work presents an extended form of the Aifantis strain-gradient plasticity theory through dependence of the plastic free energy on the Burgers tensor. The constraints of codirectiona- lity for ...the deviatoric stress and irrotationality of the plastic distortion are assumed. These provide the basis for expressing the work done by the microstress conjugate to the Bur- gers tensor as the sum of the work done by the microscopic hyperstress vector and scalar. The principle of virtual power is used to establish the microforce balance, which provides the relationship between the resolved shears, plastic microstress and the microscopic hyper- stresses. The microforce balance, when augmented with relevant constitutive relations that are consistent with the free-energy imbalance, results in a non-local flow rule depicted as a nonlinear second order partial differential equation in terms of the accumulated plastic strain with concomitant boundary conditions. It is shown in this work that the plastic mi- crostress is purely dissipative and cannot account for backstress whenever the defect energy is dependent on the Burgers tensor.
A remark on the slicing problem Giannopoulos, Apostolos; Paouris, Grigoris; Vritsiou, Beatrice-Helen
Journal of functional analysis,
02/2012, Letnik:
262, Številka:
3
Journal Article
Recenzirano
Odprti dostop
The purpose of this article is to describe a reduction of the slicing problem to the study of the parameter
I
1
(
K
,
Z
q
∘
(
K
)
)
=
∫
K
‖
〈
⋅
,
x
〉
‖
L
q
(
K
)
d
x
. We show that an upper bound of ...the form
I
1
(
K
,
Z
q
∘
(
K
)
)
⩽
C
1
q
s
n
L
K
2
, with
1
/
2
⩽
s
⩽
1
, leads to the estimate
L
n
⩽
C
2
n
4
log
n
q
1
−
s
2
,
where
L
n
:
=
max
{
L
K
:
K
is an isotropic convex body in
R
n
}
.
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