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1

A 16-node locking-free Mindlin plate resting on two-parameter elastic foundation – static and eigenvalue analysis

Buczkowski R., Taczała M., Kleiber M.

Computer Assisted Methods in Engineering and Science

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2015

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Vol. 22, no. 2

99--114

EN

The Pasternak elastic foundation model is employed to study the statics and natural frequencies of thick plates in the framework of the finite element method. A new 16-node Mindlin plate element of the Lagrange family and a 32-node zero-thickness interface element representing the response of the foundation are used in the analysis. The plate element avoids ill-conditioned behaviour due to its small thickness. In the case of the eigenvalue analysis, the equation of motion is derived by applying the Hamilton principle involving the variation of the kinetic and potential energy of the plate and foundation. Regarding the plate, the firstorder shear deformation theory is used. By employing the Lobatto numerical integration in which the integration points coincide with the element nodes, we obtain the diagonal form of the mass matrix of the plate. In practice, diagonal mass matrices are often employed due to their very attractive timeintegration schemes in explicit dynamic methods in which the inversion of the effective stiffness matrix as a linear combination of the damping and mass matrices is required. The numerical results of our analysis are verified using thin element based on the classical Kirchhoff theory and 16-node thick plate elements.

2

Stanowisko Prezydium Polskiej Akademii Nauk dotyczące gazu ziemnego znajdującego się w warstwach łupkowych (tzw. „gazu łupkowego”)

Kleiber M.

Gospodarka Surowcami Mineralnymi

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2014

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T. 30, z. 2

5--14

PL

Przedstawiono stanowisko Prezydium Polskiej Akademii Nauk dotyczące gazu ziemnego znajdującego się w warstwach łupkowych (tzw. gazu łupkowego), uchwalone w dniu 11.03.2014 r. Stanowisko zostało przygotowane na podstawie raportów cząstkowych odpowiednich Komitetów Polskiej Akademii Nauk. Przedstawia ono ocenę obecnego stanu poszukiwań złóż takiego gazu, dotychczasowego stanu rozpoznania jego zasobów, a także wybranych aspektów środowiskowych i ekonomicznych związanych z potencjalnym zagospodarowaniem złóż gazu ziemnego z formacji łupkowych w Polsce. Stanowisko prezentuje także opinię Polskiej Akademii Nauk na temat koniecznych badań naukowych i badawczo-rozwojowych, ich organizacji wspomagających poszukiwanie i rozpoznawanie złóż takiego gazu oraz potencjalne przyszłe zagospodarowanie takich złóż.

EN

The statement presented from the Presidium of the Polish Academy of Sciences, related to natural gas in shale strata (so-called shale gas), was adopted on the 11th of March, 2014. The statement was prepared on the basis of partial reports from the appropriate Committees of the Polish Academy of Sciences. It presents a concise assessment of the current state of the exploration of shale gas, the state of recognition of its resources, as well as selected environmental and economic aspects related to the potential development of shale gas resources in Poland. The statement also presents the opinion of the Polish Academy of Sciences on the scope of necessary scientific and R&D works and their organization, which should aid in the prospecting and exploration of deposits of shale gas, as well as their potential future development.

3

Normal contact stiffness of fractal rough surfaces

Buczkowski R., Kleiber M., Starzynski G.

Archives of Mechanics

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2014

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Vol. 66, nr 6

411–-428

EN

We used the fractal theory based on a single variable Weierstrass–Mandelbrot function to obtain the normal contact stiffness if rough and smooth isotropic surfaces are pressed against each other. Because in the original fractal theory the distribution of contact area is assumed geometrically, we propose the method in which the actual deformation of asperities and a correction due to asperity coupling (interaction) will be taken into account. This correction is equivalent to an increase of the effective separation by a quantity proportional to the nominal pressure and it has a significant effect on contact stiffness at larger normal loads (low separations). The numerical results demonstrate a nonlinear evolution of the contact stiffness with the normal load in particular in the first stage of loading at low squeezing pressures. We have compared the results of the theoretical contact stiffness using the fractal method with the experimental ultrasonic measurements. Experimental results made on real surfaces agree remarkably well with the theoretical predictions.

4

Efficient sampling techniques for stochastic simulation of structural systems

Stocki R., Tauzowski P., Kleiber M.

Computer Assisted Mechanics and Engineering Sciences

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2007

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Vol. 14, No. 1

127-140

EN

One of the main obstacles in making stochastic simulation a standard design tool is its high computational cost. However, this problem can be significantly reduced by using efficient sampling techniques like optimal Latin hypercube (OLH) sampling. The paper advocates this kind of approach for scatter analysis of structural responses. After explaining the idea of the OLH sampling the principal component analysis method (PCA) is briefly described. Next, on numerical examples it is shown how this technique of statistical postprocessing of simulation results can be used in the design process. Important improvements of the estimation quality offered by OLH design of experiments are illustrated on two numerical examples, one simple truss problem and one involving finite element analysis of elastic plate. Based on numerical experiments an attempt is made to propose the sample size which for a given number of random variables provides an acceptable estimation accuracy of statistical moments of system responses and which enables more advanced statistical post-processing.

5

Neural networks in solving systems of interval linear equations

Viet N. H., Kleiber M.

Foundations of Computing and Decision Sciences

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2005

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Vol. 30, No. 3

263-277

EN

In this paper, a new approach for approximating the algebraic solution of systems of interval linear equations, denoted here as SILE, is proposed. The original SILE problem is first considered in terms of an optimization problem. The exact arithmetic operations over interval numbers which appear in the cost function of this optimization problem are replaced by those performed with the use of some simple sigmoidal feed-forward neural networks. This modified cost function is then minimized using one of the gradient based algorithms. A number of numerical evaluations are provided in order to verify the proposed approach. The results are discussed and some final remarks are included.

6

Sensitivity analysis for viscoelastic bodies in object-oriented finite element environment

Tauzowski P., Kleiber M.

Computer Assisted Mechanics and Engineering Sciences

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2003

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Vol. 10, No. 2

223-238

EN

In this paper the constitutive model of thermoviscoelastic model is presented. To obtain the parameter sensitivity equations the direct differentiation method is applied. The paper also deals with the finite element for equilibrium and sensitivity analysis problems. Consistent tangent operator for the model is derived. To integrate the creep evolution equation the backward-Euler scheme is efficiently applied. The thermoviscoelastic model with parameter sensitivity analysis is implemented in object-oriented finite element system. Many advantages of the object-oriented approach in FE programming are described in the paper. Two numerical examples are solved. Very good agreement between the FE and analytical results is observed.

7

Niezawodność dużych nieliniowych układów konstrukcyjnych : wybrane studium

Postek E., Kleiber M.

Przegląd Mechaniczny

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2002

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nr 5

32-37

PL

Przedstawiono sposób postępowania podczas szacowania niezawodności dużych nieliniowych układów konstrukcyjnych, nacisk położono na zastosowanie metody różniczkowania bezpośredniego (DDM), jako przykład wybrano żelbetową konstrukcję budynku osłonowego reaktora nuklearnego.

EN

A procedure of estimation of the reliability of large non-linear structural systems. Emphasis laid on the application of the direct differentiating method (DDM). A selected example is the ferro-concrete structure of a shielding building for nuclear reactor.

8

Reliability study of a containment shell

Postek E., Siemaszko A., Kleiber M.

Journal of Theoretical and Applied Mechanics

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2002

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Vol. 40 nr 1

179-203

EN

Computational time needed for reliability analysis of realistic structural problems as a rule is very high. Improvements in efficiency are critical to allow solution of large realistic problems. The reliability analysis is usually performed using approximate First Order Reliability Method (FORM). Iterative solution procedures of FORM require extensive design sensitivity computations of high accuracy. The design of realistic structures requires computer-based numerical procedures, such as finite e,ement analysis. The design sensitivity gradients are not explicitly available in terms of design variables. The most intensive computational task of design sensitivity computation should be carried out by highly efficient and accurate methods such as discrete design sensitivity analysis. This paper describes requirements for design sensitivity information for reliability analysis. The way of coupling reliability computation with discrete AVM and DDM methods of design sensitivity analysis is pointed out. A computational program developed for layered concrete shells allows one to solve large realistic reliability problems. The reliability study of an RC nuclear containment shell is carried out. Reliability studies show which of the parameters have the highest impact on the reliability of the vessel.

PL

Analiza niezawodności dużych konstrukcji wymaga zazwyczaj bardzo długich obliczeń komputerowych. Poprawa efektywności algorytmów jest zazwyczaj warunkiem koniecznym uzyskania rozwiązań dla dużych rzeczywistych problemów. Analizę niezawodności zwykle przeprowadza się stosując przybliżoną metodę analizy niezawodności pierwszego rzędu (FORM). Procedury iteracyjne analizy niezawodności pierwszego rzędu (FORM) wymagają obliczenia gradientów wrażliwości o wysokiej dokładności. Projektowanie konstrukcji wymaga stosowania metod numerycznych takich jak metoda elementów skończonych. Gradienty wrażliwości nie są jawnie zależne od zmiennych projektowych. Obliczenia gradientów wrażliwości powinno być realizowane przy zastosowaniu efektywnych, dyskretnych metod analizy wrażliwości. W artykule przedstawiono sposób połączenia analizy niezawodności z dyskretnymi metodami obliczania gradientów wrażliwości - zmiennej sprzężonej (AVM) i różniczkowania bezpośredniego (DDM). Rozwinięty program komputerowy dla żelbetowych powłok warstwowych pozwala na rozwiązywanie dużych zadań niezawodnościowych. Przedstawiona została analiza niezawodności żelbetowego budynku bezpieczeństwa reaktora nuklearnego. Analiza niezawodności pozwala na stwierdzenie, który z parametrów projektowych ma największy wpływ na niezawodność osłony.

9

Qualitative model-based analysis of truss structures

Rosłaniec K., Kulpa Z., Kleiber M.

Computer Assisted Mechanics and Engineering Sciences

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2002

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Vol. 9, No. 1

123-133

EN

The paper discusses some methods of commonsense reasoning applicable to analysis of truss structures. The proposed method, based on qualitative representation of trusses, allows to reach conclusions in the case of highly incomplete knowledge about the system. Two cases are considered. First, when only the general geometry of the structure is known, without the quantitative knowledge of stiffness coefficients of bars. Second, with additional assumption that all stiffness coefficients of bars are roughly equal.

10

Parameter sensitivity formulation for viscoelastic structures

Tauzowski P., Kleiber M.

Computer Assisted Mechanics and Engineering Sciences

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1999

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Vol. 6, No. 2

189-203

EN

The problem of sensitivity of viscoelastic response with respect to material parameters is studied in the paper. The direct differentiation method is employed. The FEM-related implementation issues are discussed. A number of numerical examples illustrates the theory.

11

Interactive methodology for reliability-based structural design and optimization

Stocki R., Siemaszko R., Kleiber M.

Computer Assisted Mechanics and Engineering Sciences

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1999

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Vol. 6, No. 1

40-62

EN

Recent advances in reliability methods, optimization as well as design sensitivity analysis have resulted in development of computational systems supporting RBDO processes for medium/large structures. For RBDO the efficiency problems are critical and in order to get the optimum design a number of fast approximate methods have been recently proposed. These methods, tested for rather small problems, show acceptable accuracy and speed up computations considerably. However, when applied in the automated way to medium/large scale problems they may cause severe convergence problems or lead to poor local minimum after expensive computations. Instead of an automated optimization procedure, an interactive approach is proposed. Implemented in the POLSAP-RBO system it allows to combine effective interactive design methods with wisual capabilities to efficiently generate optimum design. Benchmark studies of an offshore jacket structure show efficiency of the interactive approach which employs integration, approximation and reduction techniques for maximizing efficiency of RBDO.

12

An aspect ratio condition for the buckling and folding of polymeric jets in injection mould filling

Mahomed N., Kleiber M.

Computer Assisted Mechanics and Engineering Sciences

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1998

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Vol. 5, nr 3

227-243

EN

The behaviour of planar Newtonian and Non-Newtonian polymeric jets is investigated in the context of injection mould filling. The incompressible Stokes flow model consistent with the application of injection mould filling is described together with the shear rate dependent fluid viscosity for a typical polymeric melt. The numerical procedure for the solution of the nonlinear system is briefly discussed as well as the mesh generation and the melt front tracking algorithms employed. In the analysis, the buckling behaviour of Newtonian and Non-Newtonian jets are firstly compared. There after the behaviour of Newtonian jets are analysed for various values of the aspect ratio in an attempt to study the validity of the Cruikshank buckling conditions for planar Newtonian jets. It is argued that the Reynolds number of highly viscous polymeric melts is relatively low and the aspect ratio condition is the critical condition dictating the buckling behaviour. Finally, an aspect ratio design criteria is established for buckling-free and folding-free flow of polymeric jets.