In order to address various clinical applications within living tissue, the aim of this work is to analytically study the thermomechanical interaction for a living tissue which is subjected to variable thermal loadings. Human tissues undergoing regional hyperthermia treatment for cancer therapy is based on graded changes of the cells, and as a consequences, the constitutive equations have been formulated using the nonlocal elasticity theory. The heat transport equation for the present problem is formulated in the context of Moore‐Gibson‐Thompson theory of generalized thermoelasticity assimilating the memory‐dependent derivative within a slipping interval. Both the boundaries of the tissue is maintaining the condition of zero traction. The lower boundary of the tissue is subjected to prescribed thermal loading while, the upper boundary is kept at zero temperature. Utilizing the Laplace transform mechanism, the governing equations have been solved and the general solutions have been obtained in the transformed domain. In order to arrive at the solutions in the real space‐time domain, suitable inversion of the Laplace transform has been carried out numerically using the method of Zakian. Numerical findings suggest that thermomechanical waves propagate through skin tissue over finite distances, which helps mitigate the unrealistic predictions made by the Pennes' model. Significant effect due to different effective parameter such as nonlocal parameter and the time‐delay parameter is reported. Also, how a nonlinear kernel function can be more effective in bio‐heat transfer, is outlined in the study also.
{"title":"Thermomechanical interaction in a living tissue due to variable thermal loading with memory","authors":"Ibrahim A. Abbas, Abhik Sur","doi":"10.1002/zamm.202400398","DOIUrl":"https://doi.org/10.1002/zamm.202400398","url":null,"abstract":"In order to address various clinical applications within living tissue, the aim of this work is to analytically study the thermomechanical interaction for a living tissue which is subjected to variable thermal loadings. Human tissues undergoing regional hyperthermia treatment for cancer therapy is based on graded changes of the cells, and as a consequences, the constitutive equations have been formulated using the nonlocal elasticity theory. The heat transport equation for the present problem is formulated in the context of Moore‐Gibson‐Thompson theory of generalized thermoelasticity assimilating the memory‐dependent derivative within a slipping interval. Both the boundaries of the tissue is maintaining the condition of zero traction. The lower boundary of the tissue is subjected to prescribed thermal loading while, the upper boundary is kept at zero temperature. Utilizing the Laplace transform mechanism, the governing equations have been solved and the general solutions have been obtained in the transformed domain. In order to arrive at the solutions in the real space‐time domain, suitable inversion of the Laplace transform has been carried out numerically using the method of Zakian. Numerical findings suggest that thermomechanical waves propagate through skin tissue over finite distances, which helps mitigate the unrealistic predictions made by the Pennes' model. Significant effect due to different effective parameter such as nonlocal parameter and the time‐delay parameter is reported. Also, how a nonlinear kernel function can be more effective in bio‐heat transfer, is outlined in the study also.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142178049","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}
Muhammad Irfan, Muhammad Shoaib Anwar, Metib Alghamdi, Masood Khan, Taseer Muhammad
The study of a bio‐convection is a natural progression that happens as microbes transport unsystematically in single‐celled or colony‐like environments; as they live ubiquitously, individuals, as in rodents, and plant forms. They're so much denser than liquid, owing to which, microbes develop a basis of bio‐convection. Gyrotactic microbes are individuals that dip up‐stream in contradiction of gravity in motionless liquid, producing the higher portion of the deferment to be thicker than the lesser part. Bioconvection's significance can be realized in a diversity of bio‐microsystems, for instance, bio‐tech allied to mass transport, biofuels, enzyme biosensors and fraternization. Together with nanofluids, a mixture of bioconvective is working to progress the structure's thermal enactment which has uses in diverse scientific structures. Recent study has related the progress of extrusion features, radiative heat progression and biofuel fabrication to the use of nanoparticles. The essential plans of the modern scrutinization are to examine the magneto bioconvection flow of nonlinear radiative Carreau fluid persuades by the nanofluid and Joule heating. Additionally, Convective conditions of heat, mass and motile microorganism with heat sink/source and chemical reaction have been explored. By means of similarity alteration to alter the nonlinear partial differential equations into nonlinear Ordinary differential equations (ODE). The solutions of subjected equations have been attained by exploiting the bvp4c algorithm. Homotopic algorithm has been also executed for comparison of bvp4c results and former studies. The impacts of relatable factors on diverse fields are sketched in graphic form. The study explores temperature field enhancement for thermo Biot and Brownian motion factors. Furthermore, the fluid concentration exaggerates for mass Biot and chemical reaction factor; however, declines for Brownian motion factor. The motile density field decays with the rising values for Peclet number and intensifies for motile density Biot factor. The comparison tables of current work and previous work also have been presented for the authentication of work with two different techniques.
{"title":"Modeling heat‐mass transport for MHD bio‐convection Carreau nanofluid with Joule heating containing both gyrotactic microbes and nanoparticles diffusion","authors":"Muhammad Irfan, Muhammad Shoaib Anwar, Metib Alghamdi, Masood Khan, Taseer Muhammad","doi":"10.1002/zamm.202400234","DOIUrl":"https://doi.org/10.1002/zamm.202400234","url":null,"abstract":"The study of a bio‐convection is a natural progression that happens as microbes transport unsystematically in single‐celled or colony‐like environments; as they live ubiquitously, individuals, as in rodents, and plant forms. They're so much denser than liquid, owing to which, microbes develop a basis of bio‐convection. Gyrotactic microbes are individuals that dip up‐stream in contradiction of gravity in motionless liquid, producing the higher portion of the deferment to be thicker than the lesser part. Bioconvection's significance can be realized in a diversity of bio‐microsystems, for instance, bio‐tech allied to mass transport, biofuels, enzyme biosensors and fraternization. Together with nanofluids, a mixture of bioconvective is working to progress the structure's thermal enactment which has uses in diverse scientific structures. Recent study has related the progress of extrusion features, radiative heat progression and biofuel fabrication to the use of nanoparticles. The essential plans of the modern scrutinization are to examine the magneto bioconvection flow of nonlinear radiative Carreau fluid persuades by the nanofluid and Joule heating. Additionally, Convective conditions of heat, mass and motile microorganism with heat sink/source and chemical reaction have been explored. By means of similarity alteration to alter the nonlinear partial differential equations into nonlinear Ordinary differential equations (ODE). The solutions of subjected equations have been attained by exploiting the bvp4c algorithm. Homotopic algorithm has been also executed for comparison of bvp4c results and former studies. The impacts of relatable factors on diverse fields are sketched in graphic form. The study explores temperature field enhancement for thermo Biot and Brownian motion factors. Furthermore, the fluid concentration exaggerates for mass Biot and chemical reaction factor; however, declines for Brownian motion factor. The motile density field decays with the rising values for Peclet number and intensifies for motile density Biot factor. The comparison tables of current work and previous work also have been presented for the authentication of work with two different techniques.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142178050","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 maximum angular rotation attributable to the in‐plane shear deformation of flange slabs is used as generalised displacement in the conventional analysis method for I‐beams. However, the mechanical concepts are poorly understood due to the complex nature of this analysis method. Consequently, a novel strategy for analysing vertical bending in composite I‐beams is proposed in this study. This approach uses the additional deflection of composite I‐beams induced by the shear lag effect as the generalised displacement. Furthermore, this research comprehensively considers the accordion effect, shear lag and self‐equilibrium conditions for the shear lag warping stress and bending moment. Moreover, two longitudinal warping displacement difference functions are employed to accurately describe the variation of shear lag in composite I‐beams with varying flange slab widths. The differential equations of the I‐beams with corrugated steel webs in the elastic range are established based on the energy‐variation method. A complete mechanical system of a composite I‐beam is decomposed into two parts, namely, the shear lag mechanical system and the elementary beam mechanical system, which are independent of each other. The theory presented in this paper reflects the internal mechanical mechanism of composite I‐beams. The calculation accuracy is considerably improved in this study. Therefore, this method is more unambiguous and well‐defined. It enriches and advances the current analysis theory of composite structures, which can guide the design of composite I‐beams.
{"title":"Investigating the mechanical properties related to the vertical bending of composite I‐beams with corrugated steel webs","authors":"Zi‐yu Gan, Feng Cen, Pei‐wei Gao","doi":"10.1002/zamm.202300669","DOIUrl":"https://doi.org/10.1002/zamm.202300669","url":null,"abstract":"The maximum angular rotation attributable to the in‐plane shear deformation of flange slabs is used as generalised displacement in the conventional analysis method for I‐beams. However, the mechanical concepts are poorly understood due to the complex nature of this analysis method. Consequently, a novel strategy for analysing vertical bending in composite I‐beams is proposed in this study. This approach uses the additional deflection of composite I‐beams induced by the shear lag effect as the generalised displacement. Furthermore, this research comprehensively considers the accordion effect, shear lag and self‐equilibrium conditions for the shear lag warping stress and bending moment. Moreover, two longitudinal warping displacement difference functions are employed to accurately describe the variation of shear lag in composite I‐beams with varying flange slab widths. The differential equations of the I‐beams with corrugated steel webs in the elastic range are established based on the energy‐variation method. A complete mechanical system of a composite I‐beam is decomposed into two parts, namely, the shear lag mechanical system and the elementary beam mechanical system, which are independent of each other. The theory presented in this paper reflects the internal mechanical mechanism of composite I‐beams. The calculation accuracy is considerably improved in this study. Therefore, this method is more unambiguous and well‐defined. It enriches and advances the current analysis theory of composite structures, which can guide the design of composite I‐beams.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142178047","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}
Yan Zhang, Muhammad Ramzan, Nazia Shahmir, Saad Alshahrani, Seifedine Kadry, Roobaea Alroobaea
This research seeks to explore the behavior of Ree–Eyring nanofluid over an extended surface influenced by an inclined magnetic field within a permeable medium. The local thermal non‐equilibrium between the particle, liquid, and solid phases is represented by a three‐temperature model. The problem is addressed numerically using bvp4c code in MATLAB software. The findings are displayed in the format of tables and graphs. The study shows that higher values of the interface heat transfer parameter led to a decrease and increase in the fluid phase and solid phase Nusselt number, respectively. The velocity and concentration distributions decrease with increasing porosity coefficient. Nevertheless, the fluid phase temperature distribution shows an opposing trend. Furthermore, increasing the non‐Newtonian fluid parameter leads to a raise in the surface drag coefficient.
{"title":"Analysis of thermal non‐equilibrium model on the Ree–Eyring nanofluid flow influenced by an inclined magnetic field","authors":"Yan Zhang, Muhammad Ramzan, Nazia Shahmir, Saad Alshahrani, Seifedine Kadry, Roobaea Alroobaea","doi":"10.1002/zamm.202400080","DOIUrl":"https://doi.org/10.1002/zamm.202400080","url":null,"abstract":"This research seeks to explore the behavior of Ree–Eyring nanofluid over an extended surface influenced by an inclined magnetic field within a permeable medium. The local thermal non‐equilibrium between the particle, liquid, and solid phases is represented by a three‐temperature model. The problem is addressed numerically using bvp4c code in MATLAB software. The findings are displayed in the format of tables and graphs. The study shows that higher values of the interface heat transfer parameter led to a decrease and increase in the fluid phase and solid phase Nusselt number, respectively. The velocity and concentration distributions decrease with increasing porosity coefficient. Nevertheless, the fluid phase temperature distribution shows an opposing trend. Furthermore, increasing the non‐Newtonian fluid parameter leads to a raise in the surface drag coefficient.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142178051","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 is concerned with the modeling and mathematical analysis of linear peridynamic model for arbitrary Poisson ratio's material. Based on the fundamental laws of dynamics, we re‐derive the bond‐based peridynamic model for anisotropic materials by relaxing certain assumptions. Through this process, we draw several significant conclusions, such as the relationship between the equivalent strain energy density hypothesis and the convergence of the peridynamic operator to the classical Navier operator. Additionally, the well‐posedness of time‐dependent peridynamic equations of motion is established. Finally, some necessary conditions for the material stability of anisotropic material are given.
{"title":"Re‐derivation and mathematical analysis for linear peridynamics model for arbitrary Poisson ratio's material","authors":"Shangyuan Zhang, Yufeng Nie","doi":"10.1002/zamm.202100413","DOIUrl":"https://doi.org/10.1002/zamm.202100413","url":null,"abstract":"This paper is concerned with the modeling and mathematical analysis of linear peridynamic model for arbitrary Poisson ratio's material. Based on the fundamental laws of dynamics, we re‐derive the bond‐based peridynamic model for anisotropic materials by relaxing certain assumptions. Through this process, we draw several significant conclusions, such as the relationship between the equivalent strain energy density hypothesis and the convergence of the peridynamic operator to the classical Navier operator. Additionally, the well‐posedness of time‐dependent peridynamic equations of motion is established. Finally, some necessary conditions for the material stability of anisotropic material are given.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"108 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142178052","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 paper analyzes various approximate models of geometrically nonlinear vibrations of a beam. In practice, simplified equations are often based on the quasi‐static Kirchhoff hypothesis—neglecting axial inertia. This hypothesis is justified with the prescribed end‐displacements of the beam in the axial direction. Under dead loading, quasi‐static Kirchhoff hypothesis results in a linear equation. The corresponding approximate equations obtained in this paper are based on the asymptotic procedure. The ratio of bending stiffness to reduced tensile/compressive stiffness is taken as a small parameter. Axial inertia is taken into account in the equation of the first approximation. Introduced by V.V. Bolotin concept “nonlinear inertia” is discussed. The most common errors in using the quasi‐static Kirchhoff hypothesis are analyzed.
{"title":"Asymptotic analysis of geometrically nonlinear beam vibrations: Kirchhoff and Bolotin equations","authors":"Igor V. Andrianov, Steve G. Koblik","doi":"10.1002/zamm.202400341","DOIUrl":"https://doi.org/10.1002/zamm.202400341","url":null,"abstract":"The paper analyzes various approximate models of geometrically nonlinear vibrations of a beam. In practice, simplified equations are often based on the quasi‐static Kirchhoff hypothesis—neglecting axial inertia. This hypothesis is justified with the prescribed end‐displacements of the beam in the axial direction. Under dead loading, quasi‐static Kirchhoff hypothesis results in a linear equation. The corresponding approximate equations obtained in this paper are based on the asymptotic procedure. The ratio of bending stiffness to reduced tensile/compressive stiffness is taken as a small parameter. Axial inertia is taken into account in the equation of the first approximation. Introduced by V.V. Bolotin concept “nonlinear inertia” is discussed. The most common errors in using the quasi‐static Kirchhoff hypothesis are analyzed.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142178053","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 tries to investigate the nonlinear free vibrations of the rectangular conductive elastic plate in uniform magnetic fields under the classic plate theory considering nonlinear strain‐displacement. The formulation of the governing equations integrates the electromagnetic forces arising from the motion of the plate. The nonlinear motion equations are dimensionless, which takes the effect of in‐plane inertia into account. The equations are solved by the Galerkin method and homotopy perturbation method (HPM). The effectiveness of the solution is verified. According to the solutions by HPM, the effects of the initial conditions, length‐to‐thickness ratio, and magnetic induction intensity on the nonlinear free vibrations behavior of conductive elastic plates are discussed.
{"title":"Nonlinear free vibration analysis of the rectangular conductive elastic plate in magnetic field based on homotopy perturbation method","authors":"JiaJun Gu, WeiChen Shi","doi":"10.1002/zamm.202300705","DOIUrl":"https://doi.org/10.1002/zamm.202300705","url":null,"abstract":"This article tries to investigate the nonlinear free vibrations of the rectangular conductive elastic plate in uniform magnetic fields under the classic plate theory considering nonlinear strain‐displacement. The formulation of the governing equations integrates the electromagnetic forces arising from the motion of the plate. The nonlinear motion equations are dimensionless, which takes the effect of in‐plane inertia into account. The equations are solved by the Galerkin method and homotopy perturbation method (HPM). The effectiveness of the solution is verified. According to the solutions by HPM, the effects of the initial conditions, length‐to‐thickness ratio, and magnetic induction intensity on the nonlinear free vibrations behavior of conductive elastic plates are discussed.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142178054","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}
Mehmet Giyas Sakar, Onur Saldır, Fatih Aydın, M. Yasin Rece
This article aims to achieve robust numerical results by applying the Chebyshev reproducing kernel method without homogenizing the initial‐boundary conditions of the Emden–Fowler (E‐F) equation, thereby introducing a new perspective to the literature. A novel numerical approach is presented for solving the initial‐boundary value problem of third‐order E‐F equations using Chebyshev reproducing kernel theory. Unlike previous applications, which were confined to homogeneous initial‐boundary value problems or required homogenization, the proposed method is effective for both homogeneous and nonhomogeneous cases. To handle the initial‐boundary conditions of the E‐F equations, additional basis functions are introduced rather than imposing conditions on the reproducing kernel Hilbert space. The method's effectiveness is demonstrated through five examples, which validate the theoretical analysis. Overall, the results emphasize the method's efficiency.
{"title":"A novel numerical approach for the third order Emden–Fowler type equations","authors":"Mehmet Giyas Sakar, Onur Saldır, Fatih Aydın, M. Yasin Rece","doi":"10.1002/zamm.202300640","DOIUrl":"https://doi.org/10.1002/zamm.202300640","url":null,"abstract":"This article aims to achieve robust numerical results by applying the Chebyshev reproducing kernel method without homogenizing the initial‐boundary conditions of the Emden–Fowler (E‐F) equation, thereby introducing a new perspective to the literature. A novel numerical approach is presented for solving the initial‐boundary value problem of third‐order E‐F equations using Chebyshev reproducing kernel theory. Unlike previous applications, which were confined to homogeneous initial‐boundary value problems or required homogenization, the proposed method is effective for both homogeneous and nonhomogeneous cases. To handle the initial‐boundary conditions of the E‐F equations, additional basis functions are introduced rather than imposing conditions on the reproducing kernel Hilbert space. The method's effectiveness is demonstrated through five examples, which validate the theoretical analysis. Overall, the results emphasize the method's efficiency.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142178055","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}
Fluid‐structure interaction models are used to study how a material interacts with different fluids at different Reynolds numbers. Examining the same model not only for different fluids but also for different solids allows to optimize the choice of materials for construction even better. A possible answer to this demand is parameter‐dependent discretization. Furthermore, low‐rank techniques can reduce the complexity needed to compute approximations to parameter‐dependent fluid‐structure interaction discretizations. Low‐rank methods have been applied to parameter‐dependent linear fluid‐structure interaction discretizations. The linearity of the operators involved allows to translate the resulting equations to a single matrix equation. The solution is approximated by a low‐rank method. In this paper, we propose a new method that extends this framework to nonlinear parameter‐dependent fluid‐structure interaction problems by means of the Newton iteration. The parameter set is split into disjoint subsets. On each subset, the Newton approximation of the problem related to the median parameter is computed and serves as initial guess for one Newton step on the whole subset. This Newton step yields a matrix equation whose solution can be approximated by a low‐rank method. The resulting method requires a smaller number of Newton steps if compared with a direct approach that applies the Newton iteration to the separate problems consecutively. In the experiments considered, the proposed method allows to compute a low‐rank approximation up to twenty times faster than by the direct approach.
{"title":"A low‐rank method for parameter‐dependent fluid‐structure interaction discretizations with hyperelasticity","authors":"Peter Benner, Thomas Richter, Roman Weinhandl","doi":"10.1002/zamm.202300562","DOIUrl":"https://doi.org/10.1002/zamm.202300562","url":null,"abstract":"Fluid‐structure interaction models are used to study how a material interacts with different fluids at different Reynolds numbers. Examining the same model not only for different fluids but also for different solids allows to optimize the choice of materials for construction even better. A possible answer to this demand is parameter‐dependent discretization. Furthermore, low‐rank techniques can reduce the complexity needed to compute approximations to parameter‐dependent fluid‐structure interaction discretizations. Low‐rank methods have been applied to parameter‐dependent linear fluid‐structure interaction discretizations. The linearity of the operators involved allows to translate the resulting equations to a single matrix equation. The solution is approximated by a low‐rank method. In this paper, we propose a new method that extends this framework to nonlinear parameter‐dependent fluid‐structure interaction problems by means of the Newton iteration. The parameter set is split into disjoint subsets. On each subset, the Newton approximation of the problem related to the median parameter is computed and serves as initial guess for one Newton step on the whole subset. This Newton step yields a matrix equation whose solution can be approximated by a low‐rank method. The resulting method requires a smaller number of Newton steps if compared with a direct approach that applies the Newton iteration to the separate problems consecutively. In the experiments considered, the proposed method allows to compute a low‐rank approximation up to twenty times faster than by the direct approach.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142178077","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}
Sleek Chang, Harish Chandra Arora, Aman Kumar, Denise‐Penelope N. Kontoni, Prashant Kumar, Nishant Raj Kapoor, Jagbir Singh
Reinforced concrete structures deteriorate due to changes in temperature, corrosion, and attacks of sulfate and chloride contents. Retrofitting techniques like fiber‐reinforced polymer (FRP) jacketing, known for their strength and corrosion resistance, are increasingly used to strengthen and retrofit deteriorated structural elements. Large rupture strain (LRS)‐FRP composite, composed of polyethylene terephthalate and polyethylene naphthalate, both of which have high tensile strength and high strain at rupture have been used in the studies of many researchers. This research aims to develop a reliable and accurate machine learning (ML) model to estimate the compressive strength of LRS‐FRP confined specimens. A total of 303 LRS‐FRP confined specimens were gathered after a thorough literature review to develop ML models, utilizing the linear regression, support vector regression, regression tree, and artificial neural network (ANN) algorithms. Additionally, 44 analytical models (AMs) were used to compare the performance of the developed ML models. The results revealed that the performance of the developed ANN model was higher among all the ML and AMs. The R‐value and the mean absolute percentage error (MAPE) value of the developed ANN model were 0.9822 and 6.17%, respectively. The sensitivity analysis results show that the height of the specimens had the highest impact followed by the diameter of the specimen, the number of FRP layers and thickness, and then the tensile strength of LRS‐FRP. The ANN‐based mathematical expression is simple and easy to use to predict the compressive strength of the LRS‐FRP strengthened specimens.
钢筋混凝土结构会因温度变化、腐蚀以及硫酸盐和氯化物的侵蚀而老化。以强度和耐腐蚀性著称的纤维增强聚合物（FRP）护套等改造技术越来越多地被用于加固和改造老化的结构构件。由聚对苯二甲酸乙二醇酯和聚萘二甲酸乙二醇酯组成的大断裂应变（LRS）-FRP 复合材料具有高抗拉强度和高断裂应变，已被许多研究人员采用。本研究旨在开发一种可靠、准确的机器学习（ML）模型，用于估算 LRS-FRP 承压试样的抗压强度。在全面查阅文献后，共收集了 303 个 LRS-FRP 承压试样，并利用线性回归、支持向量回归、回归树和人工神经网络 (ANN) 算法开发了 ML 模型。此外，还使用了 44 个分析模型（AM）来比较已开发 ML 模型的性能。结果显示，在所有 ML 和 AM 中，所开发的 ANN 模型性能更高。所开发的 ANN 模型的 R 值和平均绝对百分比误差 (MAPE) 值分别为 0.9822 和 6.17%。灵敏度分析结果表明，试样高度的影响最大，其次是试样直径、玻璃钢层数和厚度，然后是 LRS-FRP 的抗拉强度。基于 ANN 的数学表达式简单易用，可用于预测 LRS-FRP 加固试样的抗压强度。
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