Critical velocities of a single-layer tube of a transversely isotropic material and a two-layer composite tube consisting of two perfectly-bonded cylindrical layers of dissimilar transversely isotropic materials are analytically determined using the potential function method of Elliott in three-dimensional (3-D) elasticity. The displacement and stress components in each transversely isotropic layer of the tube subjected to a uniform internal pressure moving at a constant velocity are derived in integral forms by applying the Fourier transform method. The solution includes those for a tube composed of two dissimilar cubic or isotropic materials as special cases. In addition, it is shown that the model for the two-layer composite tube can be reduced to that for the single-layer tube. Closed-form expressions for four critical velocities are derived for the single-layer tube. The lowest critical velocity is obtained from plotting the velocity curve and finding the inflection point for both the single-layer and two-layer composite tubes. To illustrate the newly developed models, two cases are studied as examples – one for a single-layer isotropic steel tube and the other for a two-layer composite tube consisting of an isotropic steel inner layer and a transversely isotropic glass-epoxy outer layer. The numerical values of the lowest critical velocity predicted by the new 3-D elasticity-based models are obtained and compared with those given by existing models based on thin- and thick-shell theories.
{"title":"Critical Velocities of Single-layer and Two-layer Composite Tubes of Transversely Isotropic Materials Based on a Potential Function Method in 3-D Elasticity","authors":"Xin-Lin Gao","doi":"10.1115/1.4065567","DOIUrl":"https://doi.org/10.1115/1.4065567","url":null,"abstract":"\u0000 Critical velocities of a single-layer tube of a transversely isotropic material and a two-layer composite tube consisting of two perfectly-bonded cylindrical layers of dissimilar transversely isotropic materials are analytically determined using the potential function method of Elliott in three-dimensional (3-D) elasticity. The displacement and stress components in each transversely isotropic layer of the tube subjected to a uniform internal pressure moving at a constant velocity are derived in integral forms by applying the Fourier transform method. The solution includes those for a tube composed of two dissimilar cubic or isotropic materials as special cases. In addition, it is shown that the model for the two-layer composite tube can be reduced to that for the single-layer tube. Closed-form expressions for four critical velocities are derived for the single-layer tube. The lowest critical velocity is obtained from plotting the velocity curve and finding the inflection point for both the single-layer and two-layer composite tubes. To illustrate the newly developed models, two cases are studied as examples – one for a single-layer isotropic steel tube and the other for a two-layer composite tube consisting of an isotropic steel inner layer and a transversely isotropic glass-epoxy outer layer. The numerical values of the lowest critical velocity predicted by the new 3-D elasticity-based models are obtained and compared with those given by existing models based on thin- and thick-shell theories.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"85 23","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141116423","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}
Dongcan Ji, Shaotong Dong, Yunfan Zhu, Min Li, Xuanqing Fan, Yuhang Li
Knitting is a technology that has a thousand-year-old history, and can be normally seen in our daily lives. The knitted structure is constructed by the interwoven yarns that constrained by themselves, exhibiting extreme stretchability. The mechanical properties of the knit fabric also enable their integration with the flexible electronic devices. Nonetheless, it is yet problematic to expose the mechanical behaviors of knitting intrinsically. This paper investigates the mechanical characteristics of knitted structures subjected to uniaxial stretching. The analysis includes a structural assessment of the unit cell, with a focus on half of the cell accounting for symmetry. Mechanical analysis for three distinct scenarios (without elongation and friction, with elongation and no friction, with elongation and friction) is also presented. The stress-strain curve of the knitted structure and the correlation between stiffness and geometric parameters are illustrated. Additionally, simulations are carried out based on finite element analysis, yielding consistent results with the theoretical calculations. Subsequently, a uniaxial stretching experiment is conducted, and the experimental outcomes also verifies the theoretical analysis. Our analysis successfully explains the mechanical behavior of knitted structures, and also provides a reference for studying knitted fabrics with other topologies.
{"title":"Theoretical analysis for the mechanical properties of the knitted structures","authors":"Dongcan Ji, Shaotong Dong, Yunfan Zhu, Min Li, Xuanqing Fan, Yuhang Li","doi":"10.1115/1.4065476","DOIUrl":"https://doi.org/10.1115/1.4065476","url":null,"abstract":"\u0000 Knitting is a technology that has a thousand-year-old history, and can be normally seen in our daily lives. The knitted structure is constructed by the interwoven yarns that constrained by themselves, exhibiting extreme stretchability. The mechanical properties of the knit fabric also enable their integration with the flexible electronic devices. Nonetheless, it is yet problematic to expose the mechanical behaviors of knitting intrinsically. This paper investigates the mechanical characteristics of knitted structures subjected to uniaxial stretching. The analysis includes a structural assessment of the unit cell, with a focus on half of the cell accounting for symmetry. Mechanical analysis for three distinct scenarios (without elongation and friction, with elongation and no friction, with elongation and friction) is also presented. The stress-strain curve of the knitted structure and the correlation between stiffness and geometric parameters are illustrated. Additionally, simulations are carried out based on finite element analysis, yielding consistent results with the theoretical calculations. Subsequently, a uniaxial stretching experiment is conducted, and the experimental outcomes also verifies the theoretical analysis. Our analysis successfully explains the mechanical behavior of knitted structures, and also provides a reference for studying knitted fabrics with other topologies.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"54 s58","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141009223","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}
Variational integrators play a pivotal role in the simulation and control of constrained mechanical systems. Recognizing the need for a Lagrange-multiplier-free approach in such systems, this study introduces a novel method for constructing variational integrators on manifolds. Our approach unfolds in three key steps: (1) local parameterization of configuration space; (2) formulation of forced discrete Euler-Lagrange equations on manifolds; (3) derivation and implementation of highorder variational integrators. Numerical tests are conducted for both conservative and forced mechanical systems, demonstrating the excellent global energy behavior of the proposed variational integrators.
{"title":"Variational integrators on manifolds for constrained mechanical systems","authors":"Ziying Lin, Hongcheng Li, Ye Ding, Xiangyang Zhu","doi":"10.1115/1.4065477","DOIUrl":"https://doi.org/10.1115/1.4065477","url":null,"abstract":"\u0000 Variational integrators play a pivotal role in the simulation and control of constrained mechanical systems. Recognizing the need for a Lagrange-multiplier-free approach in such systems, this study introduces a novel method for constructing variational integrators on manifolds. Our approach unfolds in three key steps: (1) local parameterization of configuration space; (2) formulation of forced discrete Euler-Lagrange equations on manifolds; (3) derivation and implementation of highorder variational integrators. Numerical tests are conducted for both conservative and forced mechanical systems, demonstrating the excellent global energy behavior of the proposed variational integrators.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"40 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141010578","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}
Topology optimization is a powerful tool for structural design, while its computational cost is quite high due to the large number of design variables, especially for multi-material systems. Herein, an incremental interpolation approach with discrete cosine series expansion (DCSE) is established for multi-material topology optimization. A step function with shape coefficients (i.e., ensuring that no extra variables are required as the number of materials increases) and the use of the DCSE together reduces the number of variables (e.g., from 8400 to 120 for the optimization of the clamped-clamped beam with four materials). Remarkably, the proposed approach can effectively bypass the checkerboard problem without using any filter. The enhanced computational efficiency (e.g., a ∼89.2% reduction in computation time from 439.1 s to 47.4 s) of the proposed approach is validated via both 2D and 3D numerical cases.
{"title":"An incremental interpolation scheme with discrete cosine series expansion for multi-material topology optimization","authors":"Zhanyu Wang, Xiaonan Hu, Hongyan Wang, Qingliang Zeng, Renheng Bo, Daining Fang","doi":"10.1115/1.4065404","DOIUrl":"https://doi.org/10.1115/1.4065404","url":null,"abstract":"\u0000 Topology optimization is a powerful tool for structural design, while its computational cost is quite high due to the large number of design variables, especially for multi-material systems. Herein, an incremental interpolation approach with discrete cosine series expansion (DCSE) is established for multi-material topology optimization. A step function with shape coefficients (i.e., ensuring that no extra variables are required as the number of materials increases) and the use of the DCSE together reduces the number of variables (e.g., from 8400 to 120 for the optimization of the clamped-clamped beam with four materials). Remarkably, the proposed approach can effectively bypass the checkerboard problem without using any filter. The enhanced computational efficiency (e.g., a ∼89.2% reduction in computation time from 439.1 s to 47.4 s) of the proposed approach is validated via both 2D and 3D numerical cases.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"21 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140655991","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}
Sreehari Rajan Kattil, Yuri Bazilevs, Michael A. Sutton, S. Sockalingam, Karan Kodagali, Tusit Weerasooriya, S. Alexander
A direct approach is developed using Streamline Upwind Petrov Galerkin (SUPG) concepts to determine the spatially varying property distribution in a nominally heterogenous material. The approach is based on successful development of a SUPG-stabilized inverse finite element approach to solve the differential equations of equilibrium in terms of material properties, resulting in a matrix form [A] {E} = {R}, where [A] is a known function of measured axial strains (e.g., from StereoDIC) and axial positions, {R} is a known function of axial body forces, applied loads and reactions, and {E} is a vector of unknown material properties at discrete axial locations. Theoretical and computational developments for the SUPG-stabilized approach are described in detail for one-dimensional applications (e.g., heterogeneous tensile/compression specimens, tensile/compressive surfaces of beams). Property predictions using the SUPG method with analytic strains and additive Gaussian noise are shown to be in excellent agreement with known property values, whereas predictions using the classical Bubnov-Galerkin method exhibit large, spurious oscillations in the predicted material properties. To demonstrate the methodology using experimental measurements, a 3D printed heterogeneous tensile specimen with independently measured material properties is tested and full-field strains measured at several load levels. Results confirm that SUPG finite element property predictions are in very good agreement with independently determined values at each load level along the specimen length, providing confidence that the SUPG FE analysis framework developed in this work is stable and extendable to multiple dimensions.
{"title":"SUPG-Based Finite Element Method for Direct Material Property Determination Utilizing Full-Field Deformation Measurements","authors":"Sreehari Rajan Kattil, Yuri Bazilevs, Michael A. Sutton, S. Sockalingam, Karan Kodagali, Tusit Weerasooriya, S. Alexander","doi":"10.1115/1.4065337","DOIUrl":"https://doi.org/10.1115/1.4065337","url":null,"abstract":"\u0000 A direct approach is developed using Streamline Upwind Petrov Galerkin (SUPG) concepts to determine the spatially varying property distribution in a nominally heterogenous material. The approach is based on successful development of a SUPG-stabilized inverse finite element approach to solve the differential equations of equilibrium in terms of material properties, resulting in a matrix form [A] {E} = {R}, where [A] is a known function of measured axial strains (e.g., from StereoDIC) and axial positions, {R} is a known function of axial body forces, applied loads and reactions, and {E} is a vector of unknown material properties at discrete axial locations. Theoretical and computational developments for the SUPG-stabilized approach are described in detail for one-dimensional applications (e.g., heterogeneous tensile/compression specimens, tensile/compressive surfaces of beams). Property predictions using the SUPG method with analytic strains and additive Gaussian noise are shown to be in excellent agreement with known property values, whereas predictions using the classical Bubnov-Galerkin method exhibit large, spurious oscillations in the predicted material properties. To demonstrate the methodology using experimental measurements, a 3D printed heterogeneous tensile specimen with independently measured material properties is tested and full-field strains measured at several load levels. Results confirm that SUPG finite element property predictions are in very good agreement with independently determined values at each load level along the specimen length, providing confidence that the SUPG FE analysis framework developed in this work is stable and extendable to multiple dimensions.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":" 72","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140691941","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}
Yujia Zhang, Jiajia Shen, Yao Yan, Jingzhong Tong, Lei Zhang, Yang Liu
Compared to traditional robotic systems, small-scale robots, ranging from several millimetres to micrometres in size, are capable of reaching narrower and vulnerable regions with minimal damage. However, conventional small-scale robots' limited maneuverability and controlability hinder their ability to effectively navigate in the intricate environments, such as the gastrointestinal tract. Self-propelled capsule robots driven by vibrations and impacts emerge as a promising solution, holding the potentials to enhance diagnostic accuracy, enable targeted drug delivery, and alleviate patient discomfort during gastrointestinal endoscopic procedures. This paper builds upon our previous work on self-propelled capsule robots, exploring the potential of nonlinear connecting springs to enhance its propulsion capabilities. Leveraging a mathematical model for self-propelling robots with a von Mises truss spring, which is verified using a finite element model, we investigate the effects of negative stiffness and snap-back within the nonlinear structural spring on the robots' propelling speed. Our analysis reveals that the negative stiffness of the von Mises truss can significantly reduce the sensitivity of the propelling speed to excitation frequency. As a result, the capsule robot exhibits a remarkably wider operational band where it maintains a high average propelling speed, surpassing its linear counterpart. This work sheds light on the potential for developing customised nonlinear structural systems for diverse scenarios in small-scale robot applications, opening up new possibilities for enhanced functionality and maneuverability in various biomedical applications.
{"title":"Enhancing the mobility of small-scale robots via nonlinear structural springs exhibiting negative stiffness","authors":"Yujia Zhang, Jiajia Shen, Yao Yan, Jingzhong Tong, Lei Zhang, Yang Liu","doi":"10.1115/1.4065339","DOIUrl":"https://doi.org/10.1115/1.4065339","url":null,"abstract":"\u0000 Compared to traditional robotic systems, small-scale robots, ranging from several millimetres to micrometres in size, are capable of reaching narrower and vulnerable regions with minimal damage. However, conventional small-scale robots' limited maneuverability and controlability hinder their ability to effectively navigate in the intricate environments, such as the gastrointestinal tract. Self-propelled capsule robots driven by vibrations and impacts emerge as a promising solution, holding the potentials to enhance diagnostic accuracy, enable targeted drug delivery, and alleviate patient discomfort during gastrointestinal endoscopic procedures. This paper builds upon our previous work on self-propelled capsule robots, exploring the potential of nonlinear connecting springs to enhance its propulsion capabilities. Leveraging a mathematical model for self-propelling robots with a von Mises truss spring, which is verified using a finite element model, we investigate the effects of negative stiffness and snap-back within the nonlinear structural spring on the robots' propelling speed. Our analysis reveals that the negative stiffness of the von Mises truss can significantly reduce the sensitivity of the propelling speed to excitation frequency. As a result, the capsule robot exhibits a remarkably wider operational band where it maintains a high average propelling speed, surpassing its linear counterpart. This work sheds light on the potential for developing customised nonlinear structural systems for diverse scenarios in small-scale robot applications, opening up new possibilities for enhanced functionality and maneuverability in various biomedical applications.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":" 23","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140690360","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}
A morphing quadrotor unmanned aerial vehicle (QUAV) possesses the remarkable ability to alter its shape, enabling it to navigate through gaps smaller than its wingspan. However, these deformations result in changes to the system's center of gravity and moment of inertia, necessitating real-time computation of each state's variations. To address this challenge, we propose a dynamic modeling approach based on the Udwadia-Kalaba (U-K) method. The morphing QUAV is divided into three separate subsystems, with the dynamic modeling for each subsystem conducted independently. Subsequently, the QUAV's deformation states and inherent structure are introduced in the form of constraints, and the constrained forces are derived using the U-K equation. By combining these analytical solutions, the model of the QUAV under continuous deformation is obtained. This approach effectively simplifies the modeling computations caused by changes in the system's center of gravity and moment of inertia during deformation. A control approach is proposed to achieve attitude stabilization and altitude control for the morphing QUAV. Ultimately, the stable motion of the morphing QUAV is validated through numerical simulations.
{"title":"A Separation Modeling Method for Morphing QUAV: Analytical Solutions for Constraint Forces Under Deformation","authors":"Fangfang Dong, Baotao Yuan, Xiaomin Zhao, Ye-Hwa Chen, Shan Chen","doi":"10.1115/1.4065340","DOIUrl":"https://doi.org/10.1115/1.4065340","url":null,"abstract":"\u0000 A morphing quadrotor unmanned aerial vehicle (QUAV) possesses the remarkable ability to alter its shape, enabling it to navigate through gaps smaller than its wingspan. However, these deformations result in changes to the system's center of gravity and moment of inertia, necessitating real-time computation of each state's variations. To address this challenge, we propose a dynamic modeling approach based on the Udwadia-Kalaba (U-K) method. The morphing QUAV is divided into three separate subsystems, with the dynamic modeling for each subsystem conducted independently. Subsequently, the QUAV's deformation states and inherent structure are introduced in the form of constraints, and the constrained forces are derived using the U-K equation. By combining these analytical solutions, the model of the QUAV under continuous deformation is obtained. This approach effectively simplifies the modeling computations caused by changes in the system's center of gravity and moment of inertia during deformation. A control approach is proposed to achieve attitude stabilization and altitude control for the morphing QUAV. Ultimately, the stable motion of the morphing QUAV is validated through numerical simulations.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":" 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140692795","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}
A homogenized elasto-plastic constitutive law (including both constitutive equations and inversed constitutive equations) is proposed in an incremental form for the particle-reinforced composites based on the flow theory of plasticity and the asymptotic homogenization method. The constitutive law can be used to predict the mixed hardening behavior of particle-reinforced composites under an arbitrary loading path if the uniaxial tensile curve of matrix materials is known. It is found that the law of particle-reinforced composites is similar in form to the law of matrix materials. There is a simple proportional relationship between the yield stress, the plastic modulus and the deviatoric back stress of particle-reinforced composites and the corresponding parameters of matrix materials, which is equal to the ratio of the shear modulus of composites to the shear modulus of matrix materials. The tangent modulus of particle-reinforced composites can be calculated using a simple arithmetic formula according to the tangent modulus of matrix materials. A numerical algorithm is suggested.
{"title":"A Constitutive Law Modelling the Mixed Hardening Behavior of Particle-Reinforced Composites","authors":"Ruo Jing Zhang, Yan Liu","doi":"10.1115/1.4065253","DOIUrl":"https://doi.org/10.1115/1.4065253","url":null,"abstract":"\u0000 A homogenized elasto-plastic constitutive law (including both constitutive equations and inversed constitutive equations) is proposed in an incremental form for the particle-reinforced composites based on the flow theory of plasticity and the asymptotic homogenization method. The constitutive law can be used to predict the mixed hardening behavior of particle-reinforced composites under an arbitrary loading path if the uniaxial tensile curve of matrix materials is known. It is found that the law of particle-reinforced composites is similar in form to the law of matrix materials. There is a simple proportional relationship between the yield stress, the plastic modulus and the deviatoric back stress of particle-reinforced composites and the corresponding parameters of matrix materials, which is equal to the ratio of the shear modulus of composites to the shear modulus of matrix materials. The tangent modulus of particle-reinforced composites can be calculated using a simple arithmetic formula according to the tangent modulus of matrix materials. A numerical algorithm is suggested.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"2 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140748248","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 problem of determining temperature distribution near a spherical cavity in an otherwise infinite medium which is under uniform heat flow is a classical problem of linear heat conduction theory. Extensive reviews of relevant work can be found in [1-5]. It is clear from these studies is that what has been achieved in this regard is largely related to cavities with highly canonical shapes, mostly spherical. Solutions of similar problems for cavities with non-canonical shapes are rare. In the present article, we consider the case of a cavity in an infinite solid in a uniform heat flow, whose shape deviates slightly from a perfectly spherical shape (hereafter called nearly spherical cavity). To the first order in the small parameter characterizing the boundary perturbation, we are able to derive closed-form expressions for the temperature field around the nearly spherical cavity for sufficiently smooth boundary perturbations that are arbitrary functions of the azimuthal and polar angles.
{"title":"Temperature Field Around Nearly Spherical Cavities in Uniform Heat Flow","authors":"Mujibur Rahman","doi":"10.1115/1.4065208","DOIUrl":"https://doi.org/10.1115/1.4065208","url":null,"abstract":"\u0000 The problem of determining temperature distribution near a spherical cavity in an otherwise infinite medium which is under uniform heat flow is a classical problem of linear heat conduction theory. Extensive reviews of relevant work can be found in [1-5]. It is clear from these studies is that what has been achieved in this regard is largely related to cavities with highly canonical shapes, mostly spherical. Solutions of similar problems for cavities with non-canonical shapes are rare. In the present article, we consider the case of a cavity in an infinite solid in a uniform heat flow, whose shape deviates slightly from a perfectly spherical shape (hereafter called nearly spherical cavity). To the first order in the small parameter characterizing the boundary perturbation, we are able to derive closed-form expressions for the temperature field around the nearly spherical cavity for sufficiently smooth boundary perturbations that are arbitrary functions of the azimuthal and polar angles.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"314 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140778451","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, a specific analysis strategy for tensegrity prism units with different complexities and different connectivity is provided. Through the nodal coordinate matrix and connectivity matrix, the equilibrium equation of the structure in self-equilibrium is established, and the equilibrium matrix can be obtained. The Singular Value Decomposition (SVD) method can be used to find the self-equilibrium configuration. The expression of the torsional angle between the upper and bottom surfaces of the prismatic tensegrity structure, which includes complexity and connectivity, can be obtained through the SVD form-finding method. According to the torsional angle formula of the stable configuration, the mechanical analysis of the single node is carried out, and the force density relationship between elements is gained. The mass, as one of the standards, can be used to evaluate the light structure. This paper also studied the minimal mass of the self-equilibrium tensegrity structure with the same complexity in different connectivity and got the minimal mass calculation formula. The six-bar tensegrity prism unit, including the topology, the force density relationship, the rest length of the element, and the minimal mass with constraints (cables yield, bars yield or buckle), is investigated in this work, which shows the feasibility of systematic analysis of prismatic structures. This paper provides a theoretical reference for prismatic tensegrity units.
{"title":"Self-equilibrium analysis and minimal mass design of tensegrity prism units","authors":"Ziying Cao, A. Luo, Yaming Feng, Heping Liu","doi":"10.1115/1.4065202","DOIUrl":"https://doi.org/10.1115/1.4065202","url":null,"abstract":"\u0000 In this paper, a specific analysis strategy for tensegrity prism units with different complexities and different connectivity is provided. Through the nodal coordinate matrix and connectivity matrix, the equilibrium equation of the structure in self-equilibrium is established, and the equilibrium matrix can be obtained. The Singular Value Decomposition (SVD) method can be used to find the self-equilibrium configuration. The expression of the torsional angle between the upper and bottom surfaces of the prismatic tensegrity structure, which includes complexity and connectivity, can be obtained through the SVD form-finding method. According to the torsional angle formula of the stable configuration, the mechanical analysis of the single node is carried out, and the force density relationship between elements is gained. The mass, as one of the standards, can be used to evaluate the light structure. This paper also studied the minimal mass of the self-equilibrium tensegrity structure with the same complexity in different connectivity and got the minimal mass calculation formula. The six-bar tensegrity prism unit, including the topology, the force density relationship, the rest length of the element, and the minimal mass with constraints (cables yield, bars yield or buckle), is investigated in this work, which shows the feasibility of systematic analysis of prismatic structures. This paper provides a theoretical reference for prismatic tensegrity units.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"100 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140370485","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}
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