Prof. Marcin Kaminski: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=26592
en-us2017 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemFri, 24 Nov 2017 09:29:00 GMTFri, 24 Nov 2017 09:29:00 GMTNew applications published by Prof. Marcin Kaminskihttp://www.mapleprimes.com/images/mapleapps.gifProf. Marcin Kaminski: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=26592
Probabilistic characteristics for the transforms of the Gaussian random variables
https://www.maplesoft.com/applications/view.aspx?SID=5660&ref=Feed
This script shows the basic probabilistic characteristics of the most popular transform on Gaussian random variables (GRVs) used in scientific and engineering applications. Each time up to the 10th order probabilistic moments as well as the coefficients of variation, skewness and kurtosis are determined symbolically for a simple GRV, its second power, further its linear and higher order polynomial transforms, truncated distribution, exponential and harmonic transforms, finally - some of their combinations. Basic probabilistic moments are sometimes plotted as the functions of expected value and standard deviation variations of the initial random input. Some parts of this script may be used for various analytical derivations on Gaussian random variables, fields and processes and they can be applied in various scientific and engineering applications. This script uses no statistics and probabilistic libraries features of MAPLE, so that all formulas are explicit here and can be further modified towards the other distributions of your choice.<img src="/view.aspx?si=5660/Gaussian.jpg" alt="Probabilistic characteristics for the transforms of the Gaussian random variables" align="left"/>This script shows the basic probabilistic characteristics of the most popular transform on Gaussian random variables (GRVs) used in scientific and engineering applications. Each time up to the 10th order probabilistic moments as well as the coefficients of variation, skewness and kurtosis are determined symbolically for a simple GRV, its second power, further its linear and higher order polynomial transforms, truncated distribution, exponential and harmonic transforms, finally - some of their combinations. Basic probabilistic moments are sometimes plotted as the functions of expected value and standard deviation variations of the initial random input. Some parts of this script may be used for various analytical derivations on Gaussian random variables, fields and processes and they can be applied in various scientific and engineering applications. This script uses no statistics and probabilistic libraries features of MAPLE, so that all formulas are explicit here and can be further modified towards the other distributions of your choice.5660Tue, 19 Feb 2008 00:00:00 ZProf. Marcin KaminskiProf. Marcin KaminskiSecond order theory of deflections for the linear elastic isotropic beams (Polish version)
https://www.maplesoft.com/applications/view.aspx?SID=5612&ref=Feed
This script has been written to demonstrate a comparison between the first and the second order theories for the elastic isotropic beams deflection. As it is known, the second order theory enables to include directly the influence of the normal forces along the beam on its deflection function. From the mathematical point of view, the differential equation adequate to the deflection function is written on the deformed configuration of this beam, so that the normal forces can play significant role in the beam strength. This script consists of the three parts - the first one describes the classsical deflection determination procedure for the single bay structure clamped at both edges and loaded with the triangular force decreasing from the right to the left end. The extra loading is applied in the form of a concentrated bending moment at the right edge of the beam. The main aim of the second section is to present the procedure related to the second order theory with a compressive force, whereas the third section is devoted to the second order model with tension.<img src="/view.aspx?si=5612/image1.jpg" alt="Second order theory of deflections for the linear elastic isotropic beams (Polish version)" align="left"/>This script has been written to demonstrate a comparison between the first and the second order theories for the elastic isotropic beams deflection. As it is known, the second order theory enables to include directly the influence of the normal forces along the beam on its deflection function. From the mathematical point of view, the differential equation adequate to the deflection function is written on the deformed configuration of this beam, so that the normal forces can play significant role in the beam strength. This script consists of the three parts - the first one describes the classsical deflection determination procedure for the single bay structure clamped at both edges and loaded with the triangular force decreasing from the right to the left end. The extra loading is applied in the form of a concentrated bending moment at the right edge of the beam. The main aim of the second section is to present the procedure related to the second order theory with a compressive force, whereas the third section is devoted to the second order model with tension.5612Tue, 22 Jan 2008 00:00:00 ZProf. Marcin KaminskiProf. Marcin KaminskiDeflection of the prismatic beams on elastic Winkler foundation (Polish version)
https://www.maplesoft.com/applications/view.aspx?SID=5611&ref=Feed
This script is entirely devoted to the static problem of a deflection of the linear elastic istotropic prismatic beams resting on the homogeneous linear elastic and isotropic foundation. It is demonstrated below how one can symbolically solve the problems of such beams consisting of one, two and three different intervals with spatially varying distributed load applied along the beam, different concentrated forces and moments. It is also possible to define some variability of the bending stiffness as well as the elastic foundation parameter as piecewise constant functions along the beam. This program is able to solve symbolically fourth order differential equations of the beam equilibrium, then - to determine the integration constants from the additional boundary and continuity conditions for the beam intervals. Finally, it computes maxima and minima of deflections, bending moments and shear forces and prepares the diagrams of all those functions. This script may be easily modified to extend the beam analysis towards the structural sensitivity studies and/or reliability analysis for the beams resting on the elastic subsoils.<img src="/view.aspx?si=5611/beamelastfoundpolish_42.jpg" alt="Deflection of the prismatic beams on elastic Winkler foundation (Polish version)" align="left"/>This script is entirely devoted to the static problem of a deflection of the linear elastic istotropic prismatic beams resting on the homogeneous linear elastic and isotropic foundation. It is demonstrated below how one can symbolically solve the problems of such beams consisting of one, two and three different intervals with spatially varying distributed load applied along the beam, different concentrated forces and moments. It is also possible to define some variability of the bending stiffness as well as the elastic foundation parameter as piecewise constant functions along the beam. This program is able to solve symbolically fourth order differential equations of the beam equilibrium, then - to determine the integration constants from the additional boundary and continuity conditions for the beam intervals. Finally, it computes maxima and minima of deflections, bending moments and shear forces and prepares the diagrams of all those functions. This script may be easily modified to extend the beam analysis towards the structural sensitivity studies and/or reliability analysis for the beams resting on the elastic subsoils.5611Tue, 22 Jan 2008 00:00:00 ZProf. Marcin KaminskiProf. Marcin KaminskiThe elastic prismatic beams on the Winkler foundation
https://www.maplesoft.com/applications/view.aspx?SID=5568&ref=Feed
This script is entirely devoted to the static problem of a deflection of the linear elastic istotropic prismatic beams resting on the homogeneous linear elastic and isotropic foundation. It is demonstrated below how one can symbolically solve the problems of such beams consisting of one, two and three different intervals with spatially varying distributed load applied along the beam, different concentrated forces and moments. It is also possible to define some variability of the bending stiffness as well as the elastic foundation parameter as piecewise constant functions along the beam. This program is able to solve symbolically fourth order differential equations of the beam equilibrium, then - to determine the integration constants from the additional boundary and continuity conditions for the beam intervals. Finally, it computes maxima and minima of deflections, bending moments and shear forces and prepares the diagrams of all those functions. This script may be easily modified to extend the beam analysis towards the structural sensitivity studies and/or reliability analysis for the beams resting on the elastic subsoils.<img src="/view.aspx?si=5568/beamelastfound_87.jpg" alt="The elastic prismatic beams on the Winkler foundation" align="left"/>This script is entirely devoted to the static problem of a deflection of the linear elastic istotropic prismatic beams resting on the homogeneous linear elastic and isotropic foundation. It is demonstrated below how one can symbolically solve the problems of such beams consisting of one, two and three different intervals with spatially varying distributed load applied along the beam, different concentrated forces and moments. It is also possible to define some variability of the bending stiffness as well as the elastic foundation parameter as piecewise constant functions along the beam. This program is able to solve symbolically fourth order differential equations of the beam equilibrium, then - to determine the integration constants from the additional boundary and continuity conditions for the beam intervals. Finally, it computes maxima and minima of deflections, bending moments and shear forces and prepares the diagrams of all those functions. This script may be easily modified to extend the beam analysis towards the structural sensitivity studies and/or reliability analysis for the beams resting on the elastic subsoils.5568Fri, 21 Dec 2007 00:00:00 ZProf. Marcin KaminskiProf. Marcin KaminskiSecond Order Theory of Deflections for the Linear Elastic Isotropic Beams
https://www.maplesoft.com/applications/view.aspx?SID=5481&ref=Feed
This script has been written to demonstrate a comparison between the first and the second order theories for the elastic isotropic beams deflection. As it is known, the second order theory enables to include directly the influence of the normal forces along the beam on its deflection function. From the mathematical point of view, the differential equation adequate to the deflection function is written on the deformed configuration of this beam, so that the normal forces can play significant role in the beam strength. This script consists of the three parts - the first one describes the classsical deflection determination procedure for the single bay structure clamped at both edges and loaded with the triangular force decreasing from the right to the left end. The extra loading is applied in the form of a concentrated bending moment at the right edge of the beam. The main aim of the second section is to present the procedure related to the second order theory with a compressive force, whereas the third section is devoted to the second order model with tension.<img src="/view.aspx?si=5481/application2_2.jpg" alt="Second Order Theory of Deflections for the Linear Elastic Isotropic Beams" align="left"/>This script has been written to demonstrate a comparison between the first and the second order theories for the elastic isotropic beams deflection. As it is known, the second order theory enables to include directly the influence of the normal forces along the beam on its deflection function. From the mathematical point of view, the differential equation adequate to the deflection function is written on the deformed configuration of this beam, so that the normal forces can play significant role in the beam strength. This script consists of the three parts - the first one describes the classsical deflection determination procedure for the single bay structure clamped at both edges and loaded with the triangular force decreasing from the right to the left end. The extra loading is applied in the form of a concentrated bending moment at the right edge of the beam. The main aim of the second section is to present the procedure related to the second order theory with a compressive force, whereas the third section is devoted to the second order model with tension.5481Thu, 08 Nov 2007 00:00:00 ZProf. Marcin KaminskiProf. Marcin KaminskiThe stochastic finite element method solver for a simple tension test
https://www.maplesoft.com/applications/view.aspx?SID=5468&ref=Feed
This Maple script enables to solve numerically the simple tension test of the linear elastic bar by the constant force P applied at its both edges. The solution is provided using the stochastic perturbation-based finite element method derived from the Taylor expansion of all random parameters in the problem. The approach illustrated below is adequate to the 10th order expansion, where the expected values, standard deviations and coefficients of variation of the tensioned edge displacement are derived analytically and can be computed according to the 2nd, 4th, 6th, 8th and 10th order expansions. The plot3d option is utilized to make a visualization of those moments at the particular nodal point of the mesh, whereas the entire methodology can be linked with the other FEM Maple programs as well. Theoretical considerations are provided in: Computers & Structures, Volume 85, Issue 10, May 2007, Generalized perturbation-based stochastic finite element method in elastostatics, by Marcin Kaminski, Elsevier Ltd.<img src="/view.aspx?si=5468//applications/images/app_image_blank_lg.jpg" alt="The stochastic finite element method solver for a simple tension test" align="left"/>This Maple script enables to solve numerically the simple tension test of the linear elastic bar by the constant force P applied at its both edges. The solution is provided using the stochastic perturbation-based finite element method derived from the Taylor expansion of all random parameters in the problem. The approach illustrated below is adequate to the 10th order expansion, where the expected values, standard deviations and coefficients of variation of the tensioned edge displacement are derived analytically and can be computed according to the 2nd, 4th, 6th, 8th and 10th order expansions. The plot3d option is utilized to make a visualization of those moments at the particular nodal point of the mesh, whereas the entire methodology can be linked with the other FEM Maple programs as well. Theoretical considerations are provided in: Computers & Structures, Volume 85, Issue 10, May 2007, Generalized perturbation-based stochastic finite element method in elastostatics, by Marcin Kaminski, Elsevier Ltd.5468Mon, 29 Oct 2007 00:00:00 ZProf. Marcin KaminskiProf. Marcin Kaminski