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1

Numerical Analysis of Crosswise Heterogeneous Covering Structures in 3D Class Structure Conditions

Krentowski J., Tribiłło R.

Acta Mechanica et Automatica

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2011

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Vol. 5, no. 4

67-70

EN

The following paper presents the results of analyses of multi-layered elements and thick constructions, as well as simplifications used for solving structures of 2D class models published in specialist literature, and compares them with a different approach involving generalization of pertinent problems into 3D classes. An error estimation method was pro-posed, together with a procedure of shaping grid's density ensuring necessary computing precision. Solving huge sets of equations allowed for practically continuous values of complex functions of stress states. Several of the presented typical examples indicate the possibility of applying the algorithms, among others, to heterogeneous structures of reinforced concrete constructions.

2

Konstruowanie rozwiązań wybranych trójwymiarowych zagadnień teorii sprężystości ośrodków niejednorodnych

Kulczycki-Żyhajło R., Bajkowski A.

Acta Mechanica et Automatica

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2010

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Vol. 4, no. 2

99-106

PL

Rozpatrzono pierwsze i drugie zagadnienie teorii sprężystości dotyczące półprzestrzeni niejednorodnej składającej się z jednorodnego podłoża i niejednorodnej warstwy wierzchniej o zmieniających się wzdłuż grubości warstwy właściwościach mechanicznych. Zaproponowano algorytm konstruowania rozwiązań trójwymiarowych równań teorii sprężystości.

EN

First and second problems of the elasticity theory is considered for a non-homogeneous half-space. The body was composed of a non-homogeneous surface layer and a homogeneous half-space. It is assumed that the mechanical properties of coating material are dependent on the depth. The algorithm of solutions to the equations of three-dimensional theory of elasticity is presented.

3

Trefftz functions for 3D stress concentration problems

Murčinková Z., Kompiš V., Štiavnicky M.

Computer Assisted Mechanics and Engineering Sciences

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2008

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Vol. 15, No. 3/4

305-318

EN

The paper deals with solution of 3D problems with stress concentration using the Trefftz functions. The modelled stress concentrators are holes and cavities of spherical and ellipsoidal shapes. Moreover, the random spherical cavity microstructure is modelled. The Method of External Finite Element Approximation (MEFEA) is applied to simulate detailed stress state of mentioned stress concentrators. This boundary-type method was developed to build special approximation fund ions that are associated with surface which causes the stress concentration. The method does not need discretization by classical finite elements, however, instead of elements the domain is divided into Trefftz type subdomains. The displacement and force boundary conditions are met only approximately whereas the governing equations are fulfilled exactly in the volume for linear elasticity, making it possible to assess accuracy in terms of error in boundary conditions.

4

Application of the Wave Based techniques for steady-state semi-infinite sound radiation analysis

Rejlek J., Pluymers B., Hepberger A., Priebsch H.-H., Demset W.

Computer Assisted Mechanics and Engineering Sciences

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2008

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Vol. 15, No. 3/4

337-351

EN

This paper reports on the development of a novel wave based prediction technique for the steady-state sound radiation analysis of three-dimensional semi-infinite problems. Instead of simple polynomial shape functions, this method adopts an indirect Trefftz approach, in which it uses the exact solutions of the governing differential equation for the field variables approximation. Since a fine discretization is no longer required, the resulting wave based models are substantially smaller than the element-based counterparts. Application of the proposed approach to various validation examples illustrates an enhanced computational efficiency as compared with element-based methods.