15 research outputs found
Application of the meshless procedure for the elastoplastic torsion of prismatic rods
In this paper torsion of prismatic bars considering elastic-plastic material behavior is studied. Based on the Saint-Venant displacement assumption and the Romberg-Osgood model for the stress-strain relation, the boundary value problem for stress function is formulated. In reality an area of cross section of a bar has two regions: elastic with linear governing equation and plastic with non-linear governing equation. In the solution procedure, the meshless procedure based on the Homotopy Analysis Method HAM connected with the Method of Fundamental Solutions (MFS) and Radial Basis Functions (RBF) is applied. The considered nonlinear partial differential equation (PDE) is transform into a hierarchy of linear inhomogeneous PDEs. The accuracy of the obtained approximate solution is controlled by the number of components of the calculate solution, while the convergence of the process is monitored by an additional parameter of the method. The advantage of the proposed meshless approach is that it does not require the generation of a mesh on the domain or its boundary, but only using a cloud of arbitrary located nodes
Application of the method of fundamental solutions for inverse problems related to the determination of elasto-plastic properties of prizmatic bar
The problem of determining the elastoplastic properties of a prismatic bar from the given relation from experiment between torsional moment MT and angle of twist per unit of rod鈥檚 length 胃 is investigated as inverse problem. Proposed method of solution of inverse problem is based on solution of some sequences of direct problem with application of the Levenberg-Marquardt iteration method. In direct problem these properties are known and torsional moment as a function of angle of twist is calculated form solution of some non-linear boundary value problem. For solution of direct problem on each iteration step the method of fundamental solutions and method of particular solutions is used for prismatic cross section of rod. The non-linear torsion problem in plastic region is solved by means of the Picard iteration
Zastosowanie metody rozwi膮za艅 podstawowych i transformacji Laplace鈥檃 do odwrotnego niestacjonarnego problemu 藕r贸de艂 ciep艂a
The paper deals with the inverse determination of heat source in an unsteady heat conduction problem. The governing equation for the unsteady Fourier heat conduction in 2D region with unknown internal heat source is known as the inverse boundary-initial-value problem. The identification of strength of the heat source is achieved by using the boundary condition, initial condition and a known value of temperature in chosen points placed inside the domain. For the solution of the inverse problem of determination of the heat source, the Laplace transformation with the method of fundamental solution and radial basis functions is proposed. Due to ill conditioning of the inverse transient heat conduction problem, the Tikhonov regularization method based on SVD and L-curve criterion was used. As the test problems, the 2D inverse boundary-initial-value problems (2D IBIVP) in region with known analytical solutions are considered.Artyku艂 dotyczy odwrotnego problemu okre艣lenia mocy 藕r贸de艂 ciep艂a dla nieustalonego zagadnienia przewodzenia ciep艂a. R贸wnanie r贸偶niczkowe nieustalonego przewodzenia ciep艂a Fouriera w obszarze dwuwymiarowym z nieznanymi wewn臋trznymi 藕r贸d艂ami ciep艂a jest znane jako odwrotny problem brzegowo-pocz膮tkowy. Przy okre艣leniu mocy 藕r贸de艂 ciep艂a korzysta si臋 z warunku brzegowego, warunku pocz膮tkowego oraz znanej warto艣ci temperatury w wybranych punktach rozmieszczonych wewn膮trz rozwa偶anego obszaru. Do rozwi膮zania odwrotnego problemu 藕r贸de艂 ciep艂a zosta艂a zaproponowana transformacja Laplace鈥檃 po艂膮czona z metod膮 rozwi膮za艅 podstawowych i promieniowymi funkcjami bazowymi. Ze wzgl臋du na z艂e uwarunkowanie problemu, w pracy zastosowano metod臋 regularyzacji Tichonowa dla rozk艂adu SVD oraz kryterium L-krzywej. Jako przyk艂ady testowe rozwa偶ono dwuwymiarowe odwrotne problemy brzegowo-pocz膮tkowe (2D IBIVP) ze znanym rozwi膮zaniem analitycznymi
Application of the meshless procedure for the elastoplastic torsion of prismatic rods
In this paper torsion of prismatic bars considering elastic-plastic material behavior is studied. Based on the Saint-Venant displacement assumption and the Romberg-Osgood model for the stress-strain relation, the boundary value problem for stress function is formulated. In reality an area of cross section of a bar has two regions: elastic with linear governing equation and plastic with non-linear governing equation. In the solution procedure, the meshless procedure based on the Homotopy Analysis Method HAM connected with the Method of Fundamental Solutions (MFS) and Radial Basis Functions (RBF) is applied. The considered nonlinear partial differential equation (PDE) is transform into a hierarchy of linear inhomogeneous PDEs. The accuracy of the obtained approximate solution is controlled by the number of components of the calculate solution, while the convergence of the process is monitored by an additional parameter of the method. The advantage of the proposed meshless approach is that it does not require the generation of a mesh on the domain or its boundary, but only using a cloud of arbitrary located nodes
The inverse determination of the thermal contact resistance components of unidirectionally reinforced composite
Odwrotne okre艣lenie obj臋to艣ciowego udzia艂u w艂贸kien we wzmocnionym kompozycie z niedoskona艂ym kontaktem termicznym pomi臋dzy sk艂adnikami
The paper considers the problem of determination of the volume fraction of fibres in an unidirectionally reinforced composite in order to provide the appropriate effective thermal conductivity. The problem formulated in such a way should be treated as an inverse heat transfer problem. The thermal conductivities of constituents (fibres and matrix) and fibres arrangement are known. The calculations are carried out for an imperfect thermal contact between the fibres and matrix.W pracy rozwa偶a si臋 problem okre艣lenia obj臋to艣ciowego udzia艂u w艂贸kien w jednokierunkowo wzmocnionym kompozycie w celu uzyskania odpowiedniego efektywnego wsp贸艂czynnika przewodzenia ciep艂a. Problem sformu艂owany w ten spos贸b jest traktowany jako odwrotny problem przewodzenia ciep艂a. Wsp贸艂czynniki przewodzenia ciep艂a sk艂adnik贸w (w艂贸kien i matrycy) oraz spos贸b u艂o偶enia w艂贸kien s膮 znane. Obliczenia s膮 wykonane dla niedoskona艂ego kontaktu termicznego pomi臋dzy w艂贸knami i matryc膮
Application of the method of fundamental solutions for inverse problems related to the determination of elasto-plastic properties of prizmatic bar
The problem of determining the elastoplastic properties of a prismatic bar from the given relation from experiment between torsional moment MT and angle of twist per unit of rod鈥檚 length 胃 is investigated as inverse problem. Proposed method of solution of inverse problem is based on solution of some sequences of direct problem with application of the Levenberg-Marquardt iteration method. In direct problem these properties are known and torsional moment as a function of angle of twist is calculated form solution of some non-linear boundary value problem. For solution of direct problem on each iteration step the method of fundamental solutions and method of particular solutions is used for prismatic cross section of rod. The non-linear torsion problem in plastic region is solved by means of the Picard iteration