Przeglądaj {{ collection }} wg Autor "Kołakowski, Zbigniew"

Teraz wyświetlane 1 - 18 z 18

Comparision of Numerical Results with Known Solutions of Buckling Problem of Pressured Shallow Spherical Shells.
(Lodz University of Technology. Faculty of Mechanical Engineering. Department Division of Dynamics., 2016) Lykhachova, Olga; Kołakowski, Zbigniew
Buckling problem of pressured shallow spherical shells is studied numerically for two types of finite elements: axisymmetric and non–axisymmetric. A very good correspondence of obtained results and known solutions is revealed in the case of clamed and hinged spherical segments for both types of finite elements. The comparison of results also shows that using non–axisymmetric finite element lets one get full pre– and post–buckling equilibrium path in the range of relative deflections w=h.
Damping behaviour of thin-walled composite columns under impact in-plane loading
(Politechnika Łódzka. Katedra Wytrzymałości Materiałów i Konstrukcji., 2012) Teter, A.; Kołakowski, Zbigniew
In this paper the analysis of the damping behaviour of thin-walled composite columns with open stiffened cross-sections subjected to in-plane pulse loading is described. The pulse loading of a rectangular shape is concerned. The discussed problem of the dynamic interactive buckling is solved by the analytical-numerical method (ANM) using the Koiter’s perturbations method. A critical value of the dynamic load factors is determined according to the Budiansky-Hutchinson’s criterion for different value of the viscous damping ratio. The detailed calculations confirm that small damping does not affect the dynamic response of the thin-walled composite columns under the impact in-plane loading.
Elastic-plastic stability of FML panel and columns of open and closed cross-section
(Lodz University of Technology Press, 2016) Kołakowski, Zbigniew; Mania, Radosław, J.
Elastooptyka i metoda elementów skończonych w mechanice pękania : wybrane problemy
(Wydawnictwo Politechniki Łódzkiej, 2007) Niezgodziński, Tadeusz; Red. nauk. Wydziału: Kapitaniak, Tomasz; Kołakowski, Zbigniew; Niezgoda, Tadeusz
The book contains results of numerical calculation and their comparison with experimental tests carried out on the specimens CT. Crack propagate until damage specimen was achieved. The angle between the direction of crack propagation and the direction of the artificial crack was measured. Author during numerical investigations compare Burzynski and Huber-MisesHencky hypothesis. The Burzynski hypothesis gives very good results for brittle materials which has different properties for tensile and compression it means that relationship between limit stress for compression Re to limit stress for tension Rm is greater than 1 (for example: epoxy resign, cast iron). Influence of relation R.!Rm on angle of crack propagation was carried out. The results of investigation gives information that for relation R.!Rm greater than 1,3 the value of angle of crack propagation is constant, and its value is about 76°. The experimental investigation is solved by photoelastic method. The numerical results were obtained using finite element method package ANSYS. The problem is solved by "element birth and death" method. Results of investigations of cracking of reinforced specimens are presented.
Free and forced oscillations of Timoshenko beam made of viscoelastic material.
(Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2011) Manevich, A.; Kołakowski, Zbigniew
Dynamics of Timoshenko's beam made of a viscoelastic material is studied. Dimensionless equations of motion are obtained, depending only on two parameters, one of which relates to the shear flexibility and the second – to the viscous internal friction. Advantages of the proposed equations are illustrated by solutions to the free and forced oscillation problems for the simplest case of hinged-hinged beams. The influence of the beam shear flexibility and viscous internal friction on the natural frequencies and the dynamic amplification factor is studied.
Global and local instability of thin-walled columns beyond the proportional limit
(Wydawnictwo Politechniki Łódzkiej, 1997) Kołakowski, Zbigniew; Kowal-Michalska, Katarzyna
The problem of global and local stability in the inelastic range for thin-walled columns is examined on the basis of the defonnation theory and the incremental theory of plasticity. Columns of closed and open cross-sections built from rectangular isotropic plates are subjected to the loading changing from unifonn compression to pure bending. A solution of elastic buckling for a thin-walled orthotropic columns based on Koiter's asymptotic method is employed to investigate the elasto-plastic buckling mode of the colunm and to detennine the critical load. The study is based on the numerical method of the transition matrix. The results of numerical calculations are presented in diagrams
Local Buckling of Thin-Walled Column of Square Cross-Section Made of In-Plane Coupled Laminate.
(Lodz University of Technology. Faculty of Mechanical Engineering. Department Division of Dynamics., 2016) Kołakowski, Zbigniew; Teter, Andrzej; Pasierbiewicz, Damian
The non–symmetric, general laminate exhibits different types of coupling between the extension, shearing, bending and twisting. For practical reasons, the in–plane coupled laminate is a particularly interesting. In this case, the coupling between shearing andextension takes place. Details calculations were performed for a short columns of square cross-section made of in–plane coupled and fully uncoupled laminate under uniform compression. Finite element method (FEM) and analytical–numerical method (ANM) were performed. In FEM analyses, the eigenbuckling problem has been solved using the Lanczos method, whereas the nonlinear buckling analysis were performed using the Newton– Raphson method and the Ritz method. In ANM analyses, the Koiter’s asymptotic theory is applied. The relationship between forces/moments and deformations/curvature were described using classical lamination theory (CLT). The coupling between in–plane shearing and extension has a significant influence on the behavior of thin–walled structures under compression.
Nośność graniczna cienkościennych słupów z centralnymi żebrami pośrednimi w ramach drugiego rzędu nieliniowego przybliżenia
(Wydawnictwo Politechniki Łódzkiej, 1997) Kołakowski, Zbigniew; Teter, A.
W pracy przeanalizowano interakcyjne wyboczenie cienkościennych słupów wzmocnionych żebrami pośrednimi. Żebra modelowano płytami. Przyjęto, że słupy są swobodnie podparte na obu końcach. Zastosowano drugi rząd nieliniowego przybliżenia asymptotycznej metody Byskowa i Hutchinsona [1] wykorzystując w obliczeniach numerycznych metodę macierzy przejścia. Analizę przeprowadzono dla różnych parametrów geometrycznych.
Podstawy wytrzymałości i stateczności płytowych konstrukcji kompozytowych
(Wydawnictwo Politechniki Łódzkiej, 2008) Kołakowski, Zbigniew; Wydział Mechaniczny. Politechnika Łódzka.; Faculty of Mechanical Engineering. Lodz University of Technology.; Wodziński, Piotr; Kapitaniak, Tomasz; Królak, Marian; Wegner, Tadeusz
Prezentowany skrypt stanowi materiał uzupełniający do podstawowego kursu wytrzymałości materiałów dla inżynierów i studentów studiów magisterskich wydziałów technicznych. Zasadniczym celem jest omówienie głównych, wybranych zagadnień mechaniki i wytrzymałości materiałów ortotropowych i kompozytowych, które mogą być następnie wykorzystane w programach metody elementów skończonych. Skrypt ten może umożliwić lepsze „zrozumienie” nowoczesnych materiałów konstrukcyjnych, jakimi są kompozyty i zachęcić do dalszego samodzielnego studiowania wiedzy na ten temat. Powyższe względy zadecydowały o wprowadzeniu zapisu co najwyżej macierzowego [...].
Some aspects of the axial extension mode in an elastic thin-walled beam-column.
(Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2012) Kołakowski, Zbigniew
The present paper deals with the influence of the axial extension mode on static and dynamic interactive buckling of a thin-walled beam-column with imperfections subjected to uniform compression when the shear lag phenomenon and distortional deformations are taken into account. A plate model (2D) is adopted for the beam-column. One- and two-dimensional models of the elements are compared, too. The structure is assumed to be simply supported at the ends. Equations of motion of the component plates are obtained from Hamilton’s Principle, taking into account all components of inertia forces. Within the frame of the first order nonlinear approximation, the dynamic problem of modal interactive buckling is solved by the transition matrix using the perturbation method and Godunov’s orthogonalization.
Static and dynamic interactive buckling of composite columns.
(Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2009) Kołakowski, Zbigniew
The static and dynamic problem of interaction of global buckling modes in compressed columns with complex open and closed cross-sections was considered in the paper. The columns made of laminate composites were assumed to be simply supported at both loaded ends. A plate model was adopted in the analysis. The equations of motion of individual pla- tes (Schokker et al., 1996; Sridharan and Benito, 1984) were obtained from Hamilton’s Principle, taking into account all components of iner- tia forces (Teter and Kołakowski, 2005). Within the frame of the first order nonlinear approximation, the dynamic problem of modal interac- tive buckling was solved by the transition matrix using a perturbation method. Distortions of cross-sections and the shear-lag phenomenon were taken into consideration in the problem solution. A modification of the quasi-bifurcation dynamic Kleiber-Kotula-Saran criterion (Kleiber et al., 1987) was proposed. A comparison of the proposed modification to the Budiansky-Hutchinson criterion (Budiansky and Hutchinson, 1966; Hutchinson and Budiansky, 1966) was presented for a rectangular pulse loading.
Static and dynamic interactive buckling regarding axial extension mode of thin-walled channel
(Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2010) Kołakowski, Zbigniew
The present paper deals with an influence of the axial extension mode on static and dynamic interactive buckling of a thin-walled channel with imperfections subjected to uniform compression when the shear lag phenomenon and distortional deformations are taken into account. A plate model is adopted for the channel. The structure is assumed to be simply supported at the ends. Equations of motion of component plates were obtained from Hamilton's principle taking into account all components of inertia forces. In the frame of first order nonlinear approximation, the dynamic problem of modal interactive buckling is solved by the transition matrix using the perturbation method and Godunov's orthogonalization.
Static Buckling of FML Columns in Elastic-Plastic Range.
(Lodz University of Technology. Faculty of Mechanical Engineering. Department Division of Dynamics., 2016) Kołakowski, Zbigniew; Kowal-Michalska, Katarzyna
The paper deals with the elasto-plastic buckling of thin-walled Fiber Metal Laminates short columns/profiles subjected to axial uniform compression. Structures of open and hollow (closed) cross-sections are considered build of at plate walls. Multilayered FML walls are considered as built of alternating layers of aluminum and fiber-glass composite. Three elastic-plastic theories are employed for constitutive relations description of aluminum layers i.e. fully elastic material behavior, the J2-deformation theory of plasticity and the J2 flow theory later both with Ramberg-Osgood formula application, whereas composite layers are assumed elastic within whole loading range. Some exemplary results determined with the application of own analytical-numerical method based on the Koiter's theory, in the Byskov and Hutchinson formulation are enclosed in the form of tables and plots.
Statics, dynamics and stability of structures. Vol. 2, Statics, dynamics and stability of structural elements and systems
(Wydawnictwo Politechniki Łódzkiej, 2012) Kołakowski, Zbigniew; Kowal-Michalska, Katarzyna; Niezgoda, Tadeusz; Trombski, Marek
Termomechanika laminatów, płyt i powłok o funkcyjnej gradacji własności
(Wydawnictwo Politechniki Łódzkiej, 2010) Jędrysiak, Jarosław; Red. nauk. Wydziału: Urban, Tadeusz; Kołakowski, Zbigniew; Wierzbicki, Ewaryst
Publikacja stanowi podsumowanie wyników uzyskanych jako rezultat modelowania matematycznego różnych zagadnień termomechanicznych dla wybranych kompozytów i struktur o funkcyjnej gradacji własności. Część wyników otrzymano w ramach prac związanych z projektem badawczym finansowanym przez Ministerstwo Nauki i Szkolnictwa Wyższego w latach 2008-2010. Rozpatrywane obiekty to laminaty, płyty i powłoki o niejednorodnej budowie, zarówno na poziomie mikro, jak i makro. W skali mikro mają one tzw. tolerancyjnie-periodyczną budowę, natomiast w skali makro charakteryzują się tzw. funkcyjną poprzeczną gradacją własności. W niniejszym opracowaniu przedstawiono matematyczne modele takich kompozytów i struktur, otrzymane przy wykorzystaniu techniki tolerancyjnego uśredniania, rozwijanej w ostatnim dwudziestoleciu. Technika ta pozwala zastąpić równania różniczkowe, opisujące zagadnienia termomechaniczne tych obiektów, o silnie oscylujących, tolerancyjnie-periodycznych, nieciągłych współczynnikach uśrednionymi równaniami różniczkowymi o współczynnikach ciągłych, wolnozmiennych. Cechą charakterystyczną wyprowadzonych równań jest uwzględnienie w nich wpływu wielkości mikrostruktury ciała na jego zachowanie. Pozwala to opisać dodatkowe efekty, takie jak na przykład zjawisko dyspersji, mające bardzo istotny wpływ na dynamikę rozważanych obiektów. W książce sformułowano i wyprowadzono uśrednione równania różniczkowe modeli tolerancyjnych: dla laminatów o porzecznej gradacji własności - przewodnictwa ciepła, elastodynamiki, termosprężystości; dla cienkich płyt a także dla powłok o porzecznej gradacji własności - dynamiki. Rozważania teoretyczne zostały zilustrowane przykładami zastosowań z zakresu: stacjonarnego i niestacjonarnego przewodnictwa ciepła w laininatach, drgań laminatów, drgań cienkich płyt.
Wibroakustyka maszyn elektrycznych z magnesami trwałymi
(Wydawnictwo Politechniki Łódzkiej, 2012) Witczak, Paweł; Red. nauk. Wydziału : Ostalczyk, Piotr; Kołakowski, Zbigniew; Łukaniszyn, Marian
This book is primarily devoted to discussing the physical basis of generation of vibration and acoustic noise of electromagnetic origin in the brushless electrical machines excited by permanent magnets. These machines, due to a very good exploitation properties, are currently produced in the whole range of power ratings - from the fraction of a watt to several megawatts. Their widespread presence in the human environment makes vibrations and following sound emission burdensome for the environment, especially at large exposure times. Minimizing these parasitic effects accompanying the process of energy conversion is an issue that creates interdisciplinary problems related to electrical engineering, mechanics and acoustics. Author's idea was to combine the features of monograph and academic textbook intended for those interested in analysis, design, and various aspects of the application of electrical machines. Therefore, for the convenience of the beginning reader, the each chapter starts from classical information on the mathematical background of the presented approach and the physics of the phenomena occurring. This will facilitate an understanding of the specialized subjects presented further. Reduction of vibration and noise in electrical machines cannot be detached from their basic function which is the energy conversion. That is why the relations linking the machine ratings with its geometry and material properties are also included in the text. The second chapter discusses the most important aspects of the theory of electromagnetic field showing how they are applied in electrical machines. The process of energy conversion is described using the integral electrical and mechanical parameters of machines. The third chapter is devoted to the presentation of the major types of construction of permanent magnet machines, with special reference to the structure of multi-phase windings. Circuit representation of electrical machines is provided in chapter four, where the lumped circuit elements are presented according to different machine topologyhaving radial, axial or tubular magnetic flux. The fundamentals of thermal calculations are also included, because they are an important element in the design of all electrical equipment. The fifth chapter introduces the concept of local magnetic energy density and its momentum flux, which are necessary for the field description of the energy conversion between electrical and mechanical domains. For this purpose, the stress tensor is used, both of magnetic and mechanical origin, describing the surface and volume force densities. The next, sixth chapter starts from basics of differential representation of linear elastic continuum. It shows, how extending solutions of elementary shapes like beam or ring, it is possible to reach the analytic expressions for forced and free vibration of stator and rotor of an electric machine. Chapter Seven closes the functional part of the monograph, in which solutions of the scalar wave equation are discussed and used to calculate the acoustic field induced by point and cylindrical sources. The analysis of results of vibration and acoustic calculations is based on the Fourier transform, whose connection with the theory of linear approximation on discrete sets is presented in chapter eight. The simple numerical examples explain the capabilities and limitations of one- and two-dimensional discrete Fourier transform used to calculate the complex spectra. The ninth chapter presents computations of mechanical vibration of systems with a finite number degrees of freedom. Particular emphasis is placed on determining the forced vibration amplitudes of so-called modal components, that is, resulting from natural vibration, both of stator and rotor of an electrical machine. It also contains the relationships between these components and spatial harmonics. The monograph is closed by the chapter ten, where it is shown how to combine the numerical solutions obtained by the finite elements method in the real domain (time-space) with the assignment of chosen components in the spectral domain (frequency-mode). The mechanism of data transfer between successive areas of analysis, namely, magnetic stress, mechanical vibration and sound emission is discussed in detail.
Wprowadzenie do techniki
(Wydawnictwo Politechniki Łódzkiej, 2016) Grądzki, Ryszard; Kazimierska-Grębosz, Marianna; Marcinkowski, Andrzej; Masiarek, Andrzej; Gralewski, Jacek; Bogusławski, Grzegorz; Grądzki, Ryszard; Politechnika Łódzka. Wydział Organizacji i Zarządzania. Instytut Nauk Społecznych i Zarządzania Technologiami. Zakład Podstaw Techniki i Ekologii Przemysłowej.; Lodz University of Technology. Faculty of Organization and Management. Institute of Social Sciences and Management of Technologies.; Kołakowski, Zbigniew; Niezgodziński, Tadeusz
X Sympozjum Stateczności Konstrukcji, Zakopane, 8-12 września 2003
(Katedra Wytrzymałości Materiałów i Konstrukcji, Politechnika Łódzka, 2003) Kowal-Michalska, Katarzyna; Kołakowski, Zbigniew