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1
Content available remote Static and free vibration analysis of thin plates of the curved edges by the boundary element method considering an alternative formulation of boundary conditions
Guminiak M.
Engineering Transactions
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2016
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Vol. 64, iss. 1
3--32
EN
A static and dynamic analysis of Kirchhoff plates is presented in this paper. The proposed approach avoids Kirchhoff forces at the plate corners and equivalent shear forces at a plate boundary. Two unknown variables are considered at the boundary element node. The governing integral equations are derived using Betti’s theorem. The rectilinear and curved boundary element of the constant type are used. The non-singular formulation of the boundary (static analysis) and boundary-domain (free vibration analysis) integral equations with one and two collocation points associated with a single constant boundary element located at a plate edge are presented. Additionally, the classic three-node isoparametric curved boundary elements are introduced in static analysis according to the non-singular approach. Static fundamental solution and B`ezine technique are applied to the free vibration analysis. To establish the plate inertial forces, a plate domain is divided into triangular or annular sub-domains associated with one suitable collocation point.
2
Content available remote Defect detection in plate structures using wavelet transformation
Knitter-Piątkowska A., Guminiak M.
Engineering Transactions
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2016
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Vol. 64, iss. 2
139--156
EN
This paper is concerned with defect detection in plate structures while considering the influence of external loads. The examined structures are based on Kirchhoff plate structures. Rectangular plate structures are considered. Plate bending is described using the boundary element method. The boundary and boundary-domain integral equations are formulated in a modified, simplified approach without the need of using a value known from the classical theory of Kirchhoff plate bending. Constant-type boundary elements in a non-singular approach are introduced. The plates are loaded with a single static concentrated force or dynamic moving force. External loading is applied at selected points along the direction parallel to one dimension of the plate. Defects are introduced by additional edges forming slots or holes in relation to the basic plate domain. Deflections and curvatures are taken into account as structural responses. Analysis of structural responses is conducted using the signal processing tool of wavelet transformation in its discrete form.
3
Content available remote An alternative approach to initial stability analysis of Kirchhoff plates resting on internal supports by the boundary element method
Guminiak M.
Engineering Transactions
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2015
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Vol. 63, iss. 3
273--296
EN
An initial stability of Kirchhoff plates supported on boundary and resting on internal supports is analysed in this paper. The internal supports are understood to be part of a plate surface or a line belonging to the plate. The proposed approach avoids Kirchhoff forces at the plate corner and equivalent shear forces at the plate boundary. Two unknown and independent variables are always considered at a boundary element node depending on the type of a plate edge such as the shear force and bending moment for a clamped edge, and the shear force and angle of rotation in normal direction for a simply-supported edge. For a free edge, the deflection and angle of rotation in normal direction are considered as two independent variables with additional angle of rotation in tangent direction which depends on boundary deflections. The two governing integral equations are derived using Betti’s theorem. These equations have the form of boundary-domain integral equations. The constant type of boundary element is used. The singular and non-singular formulations of the boundary-domain integral equations with one and two collocation points associated with a single boundary element located slightly outside of a plate edge are presented. To establish a plate curvature by double differentiation of the basic boundary-domain integral equation, the plate domain is divided into rectangular subdomains associated with suitable collocation points. According to the alternative approach, a plate curvature is also established by considering three collocation points located in close proximity to each other along a line parallel to one of the two axes of global coordinate system and establishment of appropriate difference operators.
4
Content available remote An Alternative Approach of Initial Stability Analysis of Kirchhoff Plates by the Boundary Element Method
Guminiak M.
Engineering Transactions
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2014
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Vol. 62, iss. 1
33--59
EN
An initial stability of Kirchhoff plates is analysed in the paper. Proposed approach avoids Kirchhoff forces at the plate corner and equivalent shear forces at a plate boundary. Two unknown variables are considered at the boundary element node. The governing integral equations are derived using Betti theorem. The integral equations have the form of boundary and domain integral equations. The constant type of boundary element are used. The singular and non-singular formulation of the boundary-domain integral equations with one and two collocation points associated with a single boundary element located at a plate edge are presented. To establish a plate curvature by double differentiation of basic boundary-domain integral equation, a plate domain is divided into rectangular sub-domains associated with suitable collocation points. A plate curvature can also be establish by considering three collocation points located in close proximity to each other along line pararel to one of the two axes of global coordinate system and establishment of appropriate differential operators.
5
Content available Simplified approach of free vibration analysis of plates supported in vicinity of the corners by BEM
Guminiak M.
Journal of Applied Mathematics and Computational Mechanics
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2013
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Vol. 12, nr 1
45--54
EN
Free vibration analysis of Kirchhoff plate by the Boundary Element Method is presented in the paper. The boundary integral equation are derived according to the Bettie theorem. The collocation version of BEM with non-singular approach with one and double collocation points is used. The constant type of element is introduced. Boundary suport at selected point is modelled as support in vicinity of point along single boundary element.
6
Content available Application of fundamental solutions to the static analysis of thin plates subjected to transverse and in-plane loading
Pawlak Z.
Civil and Environmental Engineering Reports
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2013
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No. 10
109--123
EN
In this paper static analysis of Kirchhoff plates is considered. A transverse and in-plane loading is taken into consideration. The Finite Strip Method is used and the suitable fundamental solutions are applied. According to the finite strip method a continuous structure is divided into a set of identical elements simply supported on opposite edges. The unknowns are deflections and transverse slope variables along the nodal lines. The finite difference formulation is applied to express the equilibrium conditions of the discrete system. This reduces the number of degrees of freedom. The solution of a difference equation of equilibrium yields the fundamental function of the considered plate strip. The fundamental solution derived in this way, can be used to solve the static problem of a finite plate in the analogous way as the boundary element method is applied for continuous systems.
PL
W pracy przedstawiono analizę statyczną płyt cienkich, obciążonych zarówno poprzecznie jak i w płaszczyźnie, z wykorzystaniem metody pasm skończonych. Zgodnie z zasadami metody pasm skończonych, ciągły i nieograniczony układ aproksymowany jest nieskończoną liczbą identycznych elementów, którymi są pasma skończone swobodnie podparte na przeciwległych bokach. Niewiadomymi są tzw. amplitudy ugięć i kątów obrotu na liniach węzłowych, czyli na brzegach swobodnych pasma skończonego. Po określeniu macierzy sztywności i macierzy geometrycznej elementu skończonego wyprowadzone zostało różnicowe równanie równowagi, które obowiązuje dla każdej linii węzłowej pomiędzy elementami. Główną zaletą tej metody jest możliwość przedstawienia warunków równowagi dla całego rozważanego układu w postaci jednego równania rekurencyjnego. Rozwiązanie wspomnianego równania dla regularnego, dyskretnego pasma płytowego nazywane jest funkcją fundamentalną. Rozwiązanie fundamentalne otrzymane w ten sposób zostało wykorzystane do rozwiązania problemu statyki płyty o skończonych wymiarach, w sposób analogiczny jak metoda elementów brzegowych w statyce układów ciągłych. Podstawową korzyścią wynikającą ze stosowania metody elementów brzegowych (BEM) oraz metody pasm skończonych (FSM) jest mniejszy nakład obliczeniowy w porównaniu z innymi, podobnymi metodami.
7
Selected problems of thin and thick plates theory in terms of BEM. Theoretical foundations and numerical comparison
Guminiak M., Litewka B.
Foundations of Civil and Environmental Engineering
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2012
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No. 15
41--90
EN
A static analysis of Kirchhoff and Reissner plates by the boundary element method has been presented in the paper. The Betti’s theorem has been used to derive the boundary integral equation. The direct version of the boundary element method has been presented.
8
The application of fundamental solutions in static analysis of thin plates resting on the internal elastic support
Pawlak Z., Guminiak M.
Foundations of Civil and Environmental Engineering
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2008
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No. 11
67-96
EN
A static analysis of Kirchhoff plates rested on the elastic internal supports has been discussed in the paper. The Finite Strip Method and Boundary Element Method have been used as an engineering tool in the analysis. Suitable fundamental solutions are applied in these method. Using BEM modified approach, there is no need to introduce the Kirchhoff forces at the plate corner and equivalent shear forces at the plate boundary. Two unknown and independent variables are considered at the boundary element node. The collocation points are located slightly outside the plate boundary, hence the quasidiagonal integrals of fundamental functions are non-singular. The constant type of boundary element has been used. According to the finite strip method a continuous structure is divided into a set of identical elements simply supported on opposite edges. The unknowns are the deflections and the transverse slope amplitudes along the nodal lines. The difference equation formulation is applied to express the equilibrium conditions of the discrete system. This reduces the number of degrees of freedom to be analyzed. The solution of one equilibrium difference equation yields the fundamental function of the considered plate strip. The fundamental solution derived in this way, can be used to solve the static problem of finite plate in analogically as in the boundary element method for continuous systems.
9
Content available remote Free vibrations analysis of thin plates by the boundary element method in non-singular approach
Guminiak M.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2007
|
Vol. 6, nr 1
75-90
EN
A free vibration analysis of Kirchhoff plates is presented in the paper. Using proposed approach, there is no need to introduce Kirchhoff forces at the plate corner and equivalent shear forces at a plate boundary. Two unknown and independent variables are considered at the boundary element node. The Bettie theorem is used to derive the boundary integral equation. The collocation version of boundary element method with "constant" type of elements is presented. The source points are located slightly outside a plate boundary, hence the quasi-diagonal integrals of fundamental functions are non-singular.
10
The free vibrations analysis of plates resting on continuous internal supports by the boundary element method
Guminiak M., Sumelka W.
Foundations of Civil and Environmental Engineering
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2007
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No. 10
69-97
EN
A free vibration analysis of Kirchhoff plates resting on continuous internal supports has been presented in the paper. Using the proposed approach, there is no need to introduce Kirchhoff forces at the plate corner and equivalent shear forces at the plate boundary. Two unknown and independent variables are considered at the boundary element node. The Bcttie theorem has been used to create the boundary integral equation. The collocation version of boundary element method with "constant" type of elements has been presented. The source points are located slightly outside the plate boundary, hence the quasi-diagonal integrals of fundamental functions are non-singular.
11
The analysis of internally supported thin plates by the boundary element method. Part 2 - Free vibration analysis
Guminiak M., Sygulski R.
Foundations of Civil and Environmental Engineering
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2007
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No. 9
43-74
EN
A free vibration analysis of internally supported Kirchhoff plates has been presented in the paper. Using the proposed approach, there is no need to introduce Kirchhoff forces at the plate corner and equivalent shear forces at the plate boundary [26], [31], [32], [34]. Two unknown and independent variables have been considered at the boundary element node. The Bettie theorem has been used to derive the boundary integral equation. The collocation version of boundary element method with elements of "constant" type has been presented. The source points are located slightly outside the plate boundary, hence the quasi-diagonal integrals of fundamental functions are non-singular [27], [31], [32], [34].
12
The analysis of internally supported thin plates by the boundary element method. Part 1 - Static analysis
Guminiak M., Sygulski R.
Foundations of Civil and Environmental Engineering
|
2007
|
No. 9
17-41
EN
A static analysis of Kirchhoff plates rested on the column supports has been presented in the paper. Using the proposed approach, there is no need to introduce Kirchhoff forces at the plate corner and equivalent shear forces at the plate boundary [14], [18], [19], [22]. Two unknown and independent variables have been considered at the boundary element node. The boundary integral equation has been derived using the Bettie theorem. The collocation points are located slightly outside a plate boundary, hence the quasi-diagonal integrals of fundamental functions are non-singular [15], [18], [19], [22], The constant types boundary element have been used.
13
The analysis of internally supported thin plates by the boundary element method. Part 3 - Initial stability analysis
Guminiak M., Jankowiak T.
Foundations of Civil and Environmental Engineering
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2007
|
No. 10
51-67
EN
An initial stability of internally supported Kirchhoff plates has been analysed in the paper. Using the proposed approach, there is no need to introduce Kirchhoff forces at the plate corner and equivalent shear forces at the plate boundary. Two unknown variables are considered at the boundary clement node. The boundary integral equation is derived using the Bettie theorem. The collocation points arc located slightly outside the plate boundary, hence the quasi-diagonal integrals of fundamental functions are non-singular. The constant type of boundary clement is used.
14
Static analysis of thin plates by the boundary element method in a non-singular approach
Guminiak M.
Foundations of Civil and Environmental Engineering
|
2007
|
No. 9
75-93
EN
The asphalt standard (PN-8-96025:2000) introduces requirements concerning weather and climatic conditions with built-in Hot Mix Asphalt (HMA). This standard is limited to lack of rainfall, ambient temperature (10°C - in layers up to 8.0 cm and 5°C -in layers above 8.0 cm) and wind speed (up to 16 m/s). Unconditional adherence to these principles means the closure of the building season as early as the end of September. However, practice shows that work carried out at lower ambient temperatures can be successful. The answer to "Why is it done this way?" can be found by analysing heat flow in the layer of the mineral-asphalt mixture submitted to environmental influences, thus allowing the scale of the impact of particular factors on heat losses in HMA to be known, and
15
The initial stability of Kirchhoff plates by the boundary element method using a modified formulation of a boundary condition
Guminiak M., Sygulski R.
Foundations of Civil and Environmental Engineering
|
2006
|
No. 7
171-186
EN
The initial stability of Kirchhoff plates has been analysed in the paper. Using the proposed approach, there is no need to introduce Kirchhoff forces at the plate corner and equivalent shear forces at a plate boundary. Two unknown variables are considered at the boundary element node. The boundary integral equations are derived using Bettie theorem. The collocation points arc located slightly outside a plate boundary, hence the quasi-diagonal integrals of fundamental functions arc non-singular. [3], [5], [6], [7], [8]. The constant type of boundary element has been used.
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