Starting from the linearized weak forms of the kinematic equation and the angular momentum balance equation of three-dimensional non-linear elasticity, a stressbased dimensional reduction procedure is presented for elastic plates. After expanding the three-dimensional non-symmetric stress tensor into power series with respect to the thickness coordinate, the translational equilibrium equations, written in terms of the expanded stress coefficients, are satisfied by introducing first-order stress functions. The symmetry of the stress field is satisfied in a weak sense by applying the material rotations as Lagrangian multipliers. The seven-field plate model developed in this way employs unmodified three-dimensional strain-stress relations. On the basis of the dimensionally reduced plate model derived, a new dual-mixed plate bending finite element model is developed and presented. The numerical performance of the hp-version plate elements is investigated through the solutions of standard plate bending problems. It is shown that the modeling error of the stress-based plate model in the energy norm is better than that of the displacement-based Kirchhoff- and Reissner-Mindlin plate models. The numerical solutions and their comparisons to reference solutions indicate that the dual-mixed hp elements are free from locking problems, in either the energy norm or the stress computations, both for h- and p-extensions, and the results obtained for the stresses are accurate and reliable even for extremely thin plates.
{"title":"Stress-based dimensional reduction and dual-mixed hp finite elements for elastic plates","authors":"E. Bertóti","doi":"10.32973/jcam.2023.001","DOIUrl":"https://doi.org/10.32973/jcam.2023.001","url":null,"abstract":"Starting from the linearized weak forms of the kinematic equation and the angular momentum balance equation of three-dimensional non-linear elasticity, a stressbased dimensional reduction procedure is presented for elastic plates. After expanding the three-dimensional non-symmetric stress tensor into power series with respect to the thickness coordinate, the translational equilibrium equations, written in terms of the expanded stress coefficients, are satisfied by introducing first-order stress functions. The symmetry of the stress field is satisfied in a weak sense by applying the material rotations as Lagrangian multipliers. The seven-field plate model developed in this way employs unmodified three-dimensional strain-stress relations. On the basis of the dimensionally reduced plate model derived, a new dual-mixed plate bending finite element model is developed and presented. The numerical performance of the hp-version plate elements is investigated through the solutions of standard plate bending problems. It is shown that the modeling error of the stress-based plate model in the energy norm is better than that of the displacement-based Kirchhoff- and Reissner-Mindlin plate models. The numerical solutions and their comparisons to reference solutions indicate that the dual-mixed hp elements are free from locking problems, in either the energy norm or the stress computations, both for h- and p-extensions, and the results obtained for the stresses are accurate and reliable even for extremely thin plates.","PeriodicalId":47168,"journal":{"name":"Journal of Applied and Computational Mechanics","volume":"62 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73386498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The formulation of a system of hierarchic models for the simulation of the mechanical response of slender elastic bodies, such as elastic rods, is considered. The present work is concerned with aspects of implementation and numerical examples. We use a finite element formulation based on the principle of minimum potential energy. The displacement fields are represented by the product of one-dimensional field functions and two-dimensional director functions. The field functions are approximated by the p-version of the finite element method. Our objective is to control both the model form errors and the errors of discretization with a view toward the development of advanced engineering applications equipped with autonomous error control procedures. We present numerical examples that illustrate the performance characteristics of the algorithm.
{"title":"Application of the p-version of FEM to hierarchic rod models with reference to mechanical contact problems","authors":"I. Páczelt, B. Szabó, A. Baksa","doi":"10.32973/jcam.2023.002","DOIUrl":"https://doi.org/10.32973/jcam.2023.002","url":null,"abstract":"The formulation of a system of hierarchic models for the simulation of the mechanical response of slender elastic bodies, such as elastic rods, is considered. The present work is concerned with aspects of implementation and numerical examples. We use a finite element formulation based on the principle of minimum potential energy. The displacement fields are represented by the product of one-dimensional field functions and two-dimensional director functions. The field functions are approximated by the p-version of the finite element method. Our objective is to control both the model form errors and the errors of discretization with a view toward the development of advanced engineering applications equipped with autonomous error control procedures. We present numerical examples that illustrate the performance characteristics of the algorithm.","PeriodicalId":47168,"journal":{"name":"Journal of Applied and Computational Mechanics","volume":"27 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75570376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The goal of the paper is to present a supplementary step called postextrapolation. When applied to the well-known method of characteristics (MOC), this assures the continuous use of the specified time steps or regular numerical grid without interpolations during computations of transients in 1D 2-phase flow in straight elastic pipes. The new method consists of two steps, the first being a typical MOC step, where the C− and C+ characteristics start from regular nodal points, allowing for the point of intersection to differ from a regular one. After defining the variables there the method transforms it corresponding to the near regular grid point, using the first derivatives contained in the original, nonlinear, governing equations, as evaluated numerically from the variables got earlier in the neighboring nodes. The procedure needs no interpolations; it deals with grid-point values only. Instead of the Courant-type stability conditions, shock-wave catching and smoothing techniques help to assure numerical stability between broad limits of parameters like the closing time of a valve and the initial gas content of the fluid. Comparison by runs with traditional codes under itemized boundary conditions and measurements on a simple TPV (tank-pipe-valve) setup show acceptable scatter.
{"title":"Post-extrapolation for specified time-step results without interpolation in MOC-based 1D hydraulic transients and gas release computations","authors":"A. A. Estuti, E. Litvai","doi":"10.32973/jcam.2023.003","DOIUrl":"https://doi.org/10.32973/jcam.2023.003","url":null,"abstract":"The goal of the paper is to present a supplementary step called postextrapolation. When applied to the well-known method of characteristics (MOC), this assures the continuous use of the specified time steps or regular numerical grid without interpolations during computations of transients in 1D 2-phase flow in straight elastic pipes. The new method consists of two steps, the first being a typical MOC step, where the C− and C+ characteristics start from regular nodal points, allowing for the point of intersection to differ from a regular one. After defining the variables there the method transforms it corresponding to the near regular grid point, using the first derivatives contained in the original, nonlinear, governing equations, as evaluated numerically from the variables got earlier in the neighboring nodes. The procedure needs no interpolations; it deals with grid-point values only. Instead of the Courant-type stability conditions, shock-wave catching and smoothing techniques help to assure numerical stability between broad limits of parameters like the closing time of a valve and the initial gas content of the fluid. Comparison by runs with traditional codes under itemized boundary conditions and measurements on a simple TPV (tank-pipe-valve) setup show acceptable scatter.","PeriodicalId":47168,"journal":{"name":"Journal of Applied and Computational Mechanics","volume":"23 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74101580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The present work focuses on the numerical investigation of micro-shock wave propagation in a two-dimensional magnetogasdynamic flow in the framework of the Dis- continuous Galerkin-Finite Element Method (DG-FEM). The Lorentz force has been im- plemented in the compressible, viscous Navier–Stokes equations as a source term using first-order spatial and fourth-order temporal Runge–Kutta discretization schemes. To in- vestigate the effect of the electrical conductivity on the micro-shock wave propagation, a two-dimensional micro-shock channel problem with hydraulic diameter of 2.5 mm, length of 82 mm, and no-slip boundary conditions at the left and at the right wall is considered as a benchmark problem. In this case, acoustic waves are generated behind after the rupture of the membrane that separates two states of the same gas originally at different pressure and density and both initially at rest. The magnetic field is taken into account as uniform and stationary throughout the microchannel, and the numerical simulations are performed in a short physical time, before the reflection of the waves on the lateral wall. A detailed parametric study of the temperature, density, pressure, and u-velocity is carried out by a variation of the electrical conductivity of the magnetogasdynamic flow, under the assumption of low magnetic Reynolds numbers. It has been found that the jumps of the acoustic waves become significantly intensified when the electrical conductivity of the gas is increased. It has also been observed that the presence of the Lorentz force causes an acceleration in the gasflow towards the outlet section of the microchannel at the low Knudsen number of 0.05. The outcome of this research work could be relevant to biomedical applications where the ability to control the flow in a microchannel has a significant impact on the development of small devices aimed to deliver pharmaceutical drugs in specific locations.
{"title":"Investigation of micro-shock waves in a planar magnetogasdynamic flow using the discontinuous Galerkin finite element method","authors":"Alberto Gallottini, L. Könözsy","doi":"10.32973/jcam.2022.006","DOIUrl":"https://doi.org/10.32973/jcam.2022.006","url":null,"abstract":"The present work focuses on the numerical investigation of micro-shock wave propagation in a two-dimensional magnetogasdynamic flow in the framework of the Dis- continuous Galerkin-Finite Element Method (DG-FEM). The Lorentz force has been im- plemented in the compressible, viscous Navier–Stokes equations as a source term using first-order spatial and fourth-order temporal Runge–Kutta discretization schemes. To in- vestigate the effect of the electrical conductivity on the micro-shock wave propagation, a two-dimensional micro-shock channel problem with hydraulic diameter of 2.5 mm, length of 82 mm, and no-slip boundary conditions at the left and at the right wall is considered as a benchmark problem. In this case, acoustic waves are generated behind after the rupture of the membrane that separates two states of the same gas originally at different pressure and density and both initially at rest. The magnetic field is taken into account as uniform and stationary throughout the microchannel, and the numerical simulations are performed in a short physical time, before the reflection of the waves on the lateral wall. A detailed parametric study of the temperature, density, pressure, and u-velocity is carried out by a variation of the electrical conductivity of the magnetogasdynamic flow, under the assumption of low magnetic Reynolds numbers. It has been found that the jumps of the acoustic waves become significantly intensified when the electrical conductivity of the gas is increased. It has also been observed that the presence of the Lorentz force causes an acceleration in the gasflow towards the outlet section of the microchannel at the low Knudsen number of 0.05. The outcome of this research work could be relevant to biomedical applications where the ability to control the flow in a microchannel has a significant impact on the development of small devices aimed to deliver pharmaceutical drugs in specific locations.","PeriodicalId":47168,"journal":{"name":"Journal of Applied and Computational Mechanics","volume":"21 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79674832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents the evaluation of the Stanford University Unstructured (SU2) open-source computational software package for a high Mach number 5 flow. The test case selected is an impinging shock wave turbulent boundary layer interaction (SWTBLI) on a flat plate where the experimental data of Sch¨ulein et al. [27] is used for validation purposes. Two turbulence models, the Spalart–Allmaras (SA) and the k-ω Shear Stress Transport (SST) within the SU2 code are evaluated in this study. Flow parameters, such as skin friction, wall pressure distribution and boundary layer profiles are compared with experimental values. The results demonstrate the performance of the SU2 code at a high Mach number flow and highlight its limitations in predicting fluid flow physics. At higher shock generator angles, the discrepancy between experimental and CFD data is more significant. Within the interaction and flow separation zones, a smaller separation bubble and delayed separation are predicted by the SA model while the k-ω SST model predicts early separation. Both models are able to predict wall pressure distribution correctly within the experimental values. However, discrepancies were observed in the prediction of skin friction due to the inability of the models to capture the boundary layer recovery after shock impingement.
{"title":"Evaluation of the SU2 Open-Source Code for a Hypersonic Flow at Mach Number 5","authors":"Jia-Ming Yeap, Z. Rana, L. Könözsy, K. Jenkins","doi":"10.32973/jcam.2022.004","DOIUrl":"https://doi.org/10.32973/jcam.2022.004","url":null,"abstract":"This paper presents the evaluation of the Stanford University Unstructured (SU2) open-source computational software package for a high Mach number 5 flow. The test case selected is an impinging shock wave turbulent boundary layer interaction (SWTBLI) on a flat plate where the experimental data of Sch¨ulein et al. [27] is used for validation purposes. Two turbulence models, the Spalart–Allmaras (SA) and the k-ω Shear Stress Transport (SST) within the SU2 code are evaluated in this study. Flow parameters, such as skin friction, wall pressure distribution and boundary layer profiles are compared with experimental values. The results demonstrate the performance of the SU2 code at a high Mach number flow and highlight its limitations in predicting fluid flow physics. At higher shock generator angles, the discrepancy between experimental and CFD data is more significant. Within the interaction and flow separation zones, a smaller separation bubble and delayed separation are predicted by the SA model while the k-ω SST model predicts early separation. Both models are able to predict wall pressure distribution correctly within the experimental values. However, discrepancies were observed in the prediction of skin friction due to the inability of the models to capture the boundary layer recovery after shock impingement.","PeriodicalId":47168,"journal":{"name":"Journal of Applied and Computational Mechanics","volume":"20 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72523122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article presents unsteady simulations of laser welding based on a rapid solidification/melting model using the ANSYS-FLUENT software package with the implementation of a UDF (User Defined Function) C code. It assumes a flat interface of liquid and gas without plasma plume, evaporation and reflection and absorption effect. In the simulations, a variety of parameters are considered with different welding speeds and laser powers. The results show that with the increase of laser power, liquid fraction and velocity, penetration depth and bead width all increase. In contrary, with the increase of welding speed, the temperature, liquid fraction, penetration depth, and bead width all decrease, while the velocity magnitude is an exception. It has also been found that the increase of welding speed distorts the pool shape and forms a long tail in temperature, liquid fraction and velocity contour. The buoyancy force did not have a significant impact on the results, while the convective term makes the velocity, temperature and liquid fraction smaller. Furthermore, the negative Marangoni shear stress makes the velocity along the height and the width direction smaller in the middle of the workpiece and larger on the edges. The simulation results show a similar tendency to that obtained by other authors. The reason for the possible differences is due to the unsteadiness of the fluid flow field and the slightly different boundary conditions imposed in the model presented here. The novelties of this work are unsteady simulations, new boundary conditions and parametric studies relevant to industrial applications.
{"title":"Modeling Rapid Solidification and Melting Processes for Multiphase Flows in a Welding Technology Application","authors":"Xin Xiong, L. Könözsy","doi":"10.32973/jcam.2022.002","DOIUrl":"https://doi.org/10.32973/jcam.2022.002","url":null,"abstract":"This article presents unsteady simulations of laser welding based on a rapid solidification/melting model using the ANSYS-FLUENT software package with the implementation of a UDF (User Defined Function) C code. It assumes a flat interface of liquid and gas without plasma plume, evaporation and reflection and absorption effect. In the simulations, a variety of parameters are considered with different welding speeds and laser powers. The results show that with the increase of laser power, liquid fraction and velocity, penetration depth and bead width all increase. In contrary, with the increase of welding speed, the temperature, liquid fraction, penetration depth, and bead width all decrease, while the velocity magnitude is an exception. It has also been found that the increase of welding speed distorts the pool shape and forms a long tail in temperature, liquid fraction and velocity contour. The buoyancy force did not have a significant impact on the results, while the convective term makes the velocity, temperature and liquid fraction smaller. Furthermore, the negative Marangoni shear stress makes the velocity along the height and the width direction smaller in the middle of the workpiece and larger on the edges. The simulation results show a similar tendency to that obtained by other authors. The reason for the possible differences is due to the unsteadiness of the fluid flow field and the slightly different boundary conditions imposed in the model presented here. The novelties of this work are unsteady simulations, new boundary conditions and parametric studies relevant to industrial applications.","PeriodicalId":47168,"journal":{"name":"Journal of Applied and Computational Mechanics","volume":"19 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74520543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Due to technological advancement, as materials with complex structures (e.g., metamaterials and foams) appear in practice there is a need to develop advanced thermal models. These are called non-Fourier equations, and all have particular mathematical properties differing from the conventional attributes of Fourier's law. The present paper discusses the thermodynamic origin of non-Fourier equations and their consequences. The second law of thermodynamics influences the relations among the material parameters, and therefore, it restricts how the temperature-dependent properties can be included in the model. Furthermore, we present the properties of initial and boundary conditions, since these are crucial in solving any practical problems and are different from the usual interpretation used for the Fourier equation.
{"title":"Mathematical aspects of non-Fourier heat equations","authors":"R. Kovács","doi":"10.32973/jcam.2022.001","DOIUrl":"https://doi.org/10.32973/jcam.2022.001","url":null,"abstract":"Due to technological advancement, as materials with complex structures (e.g., metamaterials and foams) appear in practice there is a need to develop advanced thermal models. These are called non-Fourier equations, and all have particular mathematical properties differing from the conventional attributes of Fourier's law. The present paper discusses the thermodynamic origin of non-Fourier equations and their consequences. The second law of thermodynamics influences the relations among the material parameters, and therefore, it restricts how the temperature-dependent properties can be included in the model. Furthermore, we present the properties of initial and boundary conditions, since these are crucial in solving any practical problems and are different from the usual interpretation used for the Fourier equation.","PeriodicalId":47168,"journal":{"name":"Journal of Applied and Computational Mechanics","volume":"140 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86485512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper two inequalities are presented for the torsional rigidity of homogeneous monoclinic piezoelectric beams. All results of the paper are based on the Saint-Venant theory of uniform torsion. The cross section of the considered elastic and piezoelectric beams may be simply connected or multiply connected two-dimensional bounded plane domain. Examples illustrate the proven inequality relations.
{"title":"Two Theorems on the Torsional Rigidity of Piezoelectric Beams","authors":"I. Ecsedi, Á. Lengyel","doi":"10.32973/jcam.2022.003","DOIUrl":"https://doi.org/10.32973/jcam.2022.003","url":null,"abstract":"In this paper two inequalities are presented for the torsional rigidity of homogeneous monoclinic piezoelectric beams. All results of the paper are based on the Saint-Venant theory of uniform torsion. The cross section of the considered elastic and piezoelectric beams may be simply connected or multiply connected two-dimensional bounded plane domain. Examples illustrate the proven inequality relations.","PeriodicalId":47168,"journal":{"name":"Journal of Applied and Computational Mechanics","volume":"18 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75307480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The goal of this study is to calculate the eigenvalues that provide the eigenfre- quencies and the critical loads for two heterogeneous beams with three supports: the (first) [second] beam is (fixed)[pinned] at the left end, the intermediate support is a roller while the right end of the beams can move vertically but the rotation is prevented there. The beams are referred to as FrsRp and PrsRp beams. Determination of the (eigenfrequencies) [critical loads] leads to three point eigenvalue problems associated with homogeneous boundary con- ditions. With the Green functions that belong to these eigenvalue problems we can transform them into eigenvalue problems governed by homogeneous Fredholm integral equations. The eigenvalue problems can then be reduced to algebraic eigenvalue problems that are solvable numerically by utilizing effective solution algorithms.
{"title":"Solutions for the vibration and stability problems of heterogenous beams with three supports using Green functions","authors":"L. Kiss, Messaudi Abderrazek, G. Szeidl","doi":"10.32973/jcam.2022.007","DOIUrl":"https://doi.org/10.32973/jcam.2022.007","url":null,"abstract":"The goal of this study is to calculate the eigenvalues that provide the eigenfre- quencies and the critical loads for two heterogeneous beams with three supports: the (first) [second] beam is (fixed)[pinned] at the left end, the intermediate support is a roller while the right end of the beams can move vertically but the rotation is prevented there. The beams are referred to as FrsRp and PrsRp beams. Determination of the (eigenfrequencies) [critical loads] leads to three point eigenvalue problems associated with homogeneous boundary con- ditions. With the Green functions that belong to these eigenvalue problems we can transform them into eigenvalue problems governed by homogeneous Fredholm integral equations. The eigenvalue problems can then be reduced to algebraic eigenvalue problems that are solvable numerically by utilizing effective solution algorithms.","PeriodicalId":47168,"journal":{"name":"Journal of Applied and Computational Mechanics","volume":"23 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74046951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The main aim of this paper is to construct the fundamental solutions of a system of equations for isotropic thermoelastic diffusive materials with microtemperatures and microconcentrations in the case of steady oscillations in terms of elementary functions. In addition to this, the fundamental solutions of the system of equations of equilibrium theory of isotropic thermoelastic diffusivity materials with microtemperatures and microconcentrations are also established.
{"title":"Fundamental solutions in the theory of thermoelastic diffusive materials with microtemperatures and microconcentrations","authors":"T. Kansal","doi":"10.32973/jcam.2022.005","DOIUrl":"https://doi.org/10.32973/jcam.2022.005","url":null,"abstract":"The main aim of this paper is to construct the fundamental solutions of a system of equations for isotropic thermoelastic diffusive materials with microtemperatures and microconcentrations in the case of steady oscillations in terms of elementary functions. In addition to this, the fundamental solutions of the system of equations of equilibrium theory of isotropic thermoelastic diffusivity materials with microtemperatures and microconcentrations are also established.","PeriodicalId":47168,"journal":{"name":"Journal of Applied and Computational Mechanics","volume":"40 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81567322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：