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Diagnostics of the strength and stiffness of the loader carrier system structural elements in terms of thinning of walls by numerical methods

Orobey Viktor, Nemchuk Oleksii, Lymarenko Oleksandr, Piterska Varvara, Sherstiuk Olha, Romanov Oleksandr, Tkachuk Kateryna

Diagnostyka

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2021

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Vol. 22, No. 3

73--81

EN

Modern gantry cranes are an indispensable element of large industrial and transport enterprises. Port handling equipment is operated under conditions of complex spatial loading of varying intensity, as well as under conditions when the walls of structural elements are thinned in the crane carrier system. During the operation of handling equipment in ports, at construction sites, in machine-building industries, in addition to the external load, aggressive media act on the carrier system elements, which leads to various types of wear: corrosive, abrasive and mechanical. Monitoring of the state of handling equipment structures is a very important task of diagnosing the state of the material of elements of the carrier system of cranes and transporting machines. An important and urgent scientific and technical problem of taking into account the influence of aggressive environment on the stress-strain state of the metal structures of gantry cranes is considered. It is noted that during corrosion, a significant thinning of the walls of structural elements occurs. The safety of crane operation requires this factor to be taken into account. It is proposed to use modern numerical methods for this, i.e. the boundary element method (BEM) and the finite element method (FEM). The implementation of these methods is performed in the Matlab programming and modeling environment (BEM), and the FEM is used in the Ansys package. In accordance with the technologies of these methods, the design diagrams of the lower girders and the crane structure as a whole were formed. Exact models of strain of crane elements during transverse bending and constrained torsion are given. Calculations of the stressstrain state of the crane metal structures have been performed. On the basis of a preliminary field study, a numerical model is proposed for diagnosing the strength and stiffness characteristics of the carrier system of handling equipment using the BEM and FEM, which has never been used in the world. Conclusions are drawn about the influence of the thinning of the walls of metal structures on the values of normal and tangential stresses.

2

Wspomagana komputerowo analiza wpływu zużycia zębów na stan naprężenia w ich stopach

Wilk A., Folęga P., Figlus T.

Zeszyty Naukowe. Transport / Politechnika Śląska

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2006

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z. 63

97-102

PL

W pracy przeprowadzono analizę wpływu naturalnego procesu zużycia powierzchni roboczych zębów na wartości naprężeń w ich stopach oraz karbie spowodowanym zachodzącym zużyciem. W analizie stanu naprężenia zębów kół zewnętrznie uzębionych wykorzystano metodę elementów brzegowych (MEB).

EN

The analysis of influence of wear use of working surfaces of teeth on values of stresses in their bases has been presented in the paper. The Boundary Element Method (BEM) was used in numerical analysis of the strength of the external wheel gears.

3

New Continuum Formulations for Modelling of Fiber Reinforced Composites

Zmindak M., Novák P., Melicher R.

Machine Dynamics Problems

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2006

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Vol. 30, No. 4

190-199

EN

The composites reinforced by rigid particles improve considerably many properties of matrix materials, they poses higher stiffness, strength, better wear resistance, superior electrical properties. The fibers are supposed to be much stiffer than the matrix and their diameter can be much smaller than their length. On the other side the number of the reinforcing particles can be very high and they can be not uniformly distributed over the structure. From material structure point view the particles present inclusions. For of such problems the methods like (finite element methods) FEM and BEM (boundary element methods) are not very efficient. Computational time for FEM is huge for an accurate solution of the mechanical fields. BEM using distributed forces, dislocations and dipoles along the fiber axis (the source points) enable to model these effects much more efficiently. The intensity of the source functions simulates the interaction of the fiber with the other subjects. Because of very close distance of the source points to the fiber boundary and the quasi-singular form of the integrals, the integration is performed analytically in the fiber direction. In this paper we will present two new methods for modelling composites reinforced by fibers: First proposed method is called here the method of continuous source functions (MCSF) which use continuously distributed dipoles as source functions. The second method is Boundary point method (BPM). In this method all internal fields will be approximated by the Trefftz functions (T-functions).

4

A boundary integral equation formulation of moderately thick laminated anisotropic shallow shells

Wang J., Schweizerhof K.

Applied Mechanics and Engineering

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1999

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Vol. 4, no 4

621-639

EN

In this paper, a boundary integral equation formulation of moderately thick laminated anisotropic shallow shells including transverse shear deformation is presented using the method of weighted residuals. Numerical computation of the boundary integral equation presented is discussed in detail. Some of numerical examples are given and compared with the exact solutions and the solutions available in the literature. The numerical results show that the method presented has good accuracy and high efficiency.

5

On application of the boundary element methods for analysis of shakedown problems

Cecot W.

Journal of Theoretical and Applied Mechanics

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1998

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nr 2

387-401

EN

The paper aims at presentation of the numerical model of shakedown analysis based on the direct and indirect versions of boundary element method. Comparsion of numerical results with those obtained by the finite element and finite difference methods proved the efficiency and reliability of the boundary elements. A posteriori error estimate and adaptive meshing are discussed and proposed as further improvement of the BEM shakedown analysis.

PL

W artykule opisano model numeryczny służący do rozwiązywania zagadnień dostosowania się ciał sprężysto-plastycznych do obciążeń cyklicznych. Zastosowano pośrednią i bezpośrednią wersję metody elementów brzegowych. Wyniki obliczeń numerycznych porównano z otrzymanymi przy pomocy metod elementów i różnic skończonych. Ich zgodność potwierdza skuteczność i poprawność zastosowanego podejścia. Jako dalsze usprawnienie algorytmu zaproponowano włączenia do algorytmu oszacowania a posteriori błędu obliczeń oraz adaptację siatki.

6

An analysis of the exterior Neumann problem for the Poisson equation in connection with a numerical procedure

Roliński Tomasz

Matematyka Stosowana : matematyka dla społeczeństwa

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1993

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Nr 36

3--17

EN

This paper is concerned with transforming the exterior problem Δu=f on Ωc, (∂u/∂n)|Γ=g, where ΩR2 is a bounded region and Ω^(c)=int(R2\Ω), into a problem represented by two equations. The first one is posed on a bounded domain and the second one is posed on the outer part of the boundary of the domain. This new problem is suitable for a numerical method based on coupling the finite and boundary element methods.

7

A method for solving the Neumann problem for the Poisson equation on the exterior of a poligon

Roliński Tomasz

Matematyka Stosowana : matematyka dla społeczeństwa

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1993

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Nr 36

19--40

EN

This paper is concerned with a numerical method for solving the problem Δu=f in Ωc (=intR2\Ω), (du/dn)|Γ=g, where ΩR2 is a polygon and Γ is the boundary of Ω. The method is based on coupling finite and boundary element techniques. To compensate for the loss of smoothness of the solution u near the corners of the polygon Ω we refine the triangulation without changing the number of triangles. We apply the affine triangular Lagrangean element of degree kN and the Lagrangean boundary element of degree k−1 to obtain the optimal order of convergence via the Galerkin projection.