For statically indeterminate structure, the internal force will be changed with the translation of the supports, because the internal force is related to the absolute value of the stiffness EI. When the tension is dif...For statically indeterminate structure, the internal force will be changed with the translation of the supports, because the internal force is related to the absolute value of the stiffness EI. When the tension is different with the compression modulus, EI is the function of internal force and is not constant any more that is different from classic mechanics. In the other words, it is a nonlinear problem to calculate the internal force. The expression for neutral axis of the statically indeterminate structure was derived in the paper. The iterative program for nonlinear internal force was compiled. One case study was presented to illustrate the difference between the results using the different modulus theory and the single modulus theory as in classical mechanics. Finally, some reasonable suggestions were made for the different modulus structures.展开更多
The paper presents the principles of a method, which in two simple stages makes possible to carry out the statically calculation of values of forces acting in the fiat static indeterminate trusses. In each stage, it i...The paper presents the principles of a method, which in two simple stages makes possible to carry out the statically calculation of values of forces acting in the fiat static indeterminate trusses. In each stage, it is considered the static determinate truss, scheme of which is obtained after remove the suitable number of members from the basic static indeterminate truss. The both intermediate statically determinate trusses are of the same clear span and they are loaded by forces of half values applied to the corresponding truss nodes. The method applies one of the typical procedures of calculation of the statically determinate trusses and then it is applied in an appropriate way the rule of superposition for obtaining the final values of forces acting in particular members of the basic truss. The values of forces calculated in this way are of a very close approximation to the force values determined in the special and complex ways being considered as the exact calculation methods. The proposed method can be useful mostly but not only for the initial structural design of such systems. The simplicity of the two-stage method justifies an assumption that it can be relatively easy and worthy to adjust to the requirements of the computer aided technology of statically calculation of the complex forms of trusses.展开更多
Statically indeterminate symmetric(SIS)flexure structures are symmetric structures with“clamped-clamped”boundary conditions.The static indeterminacy and topological symmetry significantly attenuate the parasitic mot...Statically indeterminate symmetric(SIS)flexure structures are symmetric structures with“clamped-clamped”boundary conditions.The static indeterminacy and topological symmetry significantly attenuate the parasitic motions associated with statically determinate flexure structures.Hence,SIS flexure structures feature decoupled linear and angular motions,improved motion accuracy,high stiffness,and high stability.Although SIS flexure structures have been more frequently utilized as prismatic joints,they can also be utilized as revolute joints.This study systematically investigates the characteristics of SIS flexure structures.Based on the unified compliance models of a single flexure hinge,analytical compliance models of two fundamental types of SIS flexure structures are established.In 1-degree-of-freedom or planar applications,multiple SIS-based structures can also be integrated into various configurations to transmit linear or angular motions.Corresponding stiffness models are also established.The characteristics and possible applications of the SIS flexure structures are computationally investigated through case studies.Ultimately,several SIS prototypes are manufactured,and the modeling accuracy of the established stiffness models is experimentally verified.展开更多
Flexure-based mechanisms are widely utilized in nano manipulations. The closed-form statics and dynamics modeling is difficult due to the complex topologies, the inevitable compliance of levers, the Hertzian contact i...Flexure-based mechanisms are widely utilized in nano manipulations. The closed-form statics and dynamics modeling is difficult due to the complex topologies, the inevitable compliance of levers, the Hertzian contact interface, etc. This paper presents the closed-form modeling of an XY nano-manipulator consisting of statically indeterminate symmetric(SIS) structures using leaf and circular flexure hinges. Theoretical analysis reveals that the lever’s compliance, the contact stiffness, and the load mass have significant influence on the static and dynamic performances of the system.Experiments are conducted to verify the effectiveness of the established models. If no piezoelectric actuator(PEA) is installed, the influence of the contact stiffness can be eliminated. Experimental results show that the estimation error on the output stiffness and first natural frequency can reach 2% and 1.7%, respectively. If PEAs are installed, the contact stiffness shows up in the models. As no effective method is currently available to measure or estimate the contact stiffness, it is impossible to precisely estimate the performance of the overall system. In this case, the established closed-form models can be utilized to calculate the bounds of the performance. The established closed-form models are widely applicable in the design and optimization of planar flexure-based mechanisms.展开更多
The paper presents general description of combined structural system and initial analysis of an innovative system proposed as the main support structure for tall or heavy loaded buildings located on subsoil of very sm...The paper presents general description of combined structural system and initial analysis of an innovative system proposed as the main support structure for tall or heavy loaded buildings located on subsoil of very small load-carrying ability or in earthquake areas. Moreover there is presented also an innovative two-stage method of the approximate calculation of the statically indeterminate trusses. Both are invented by the author by application of the principles of the superposition method.展开更多
This paper discusses the generalized variational principles founded by the technique of Lagrangian multipliers in structural mechanics and analyzes the nonlinear statically indeterminate structures. It is assumed that...This paper discusses the generalized variational principles founded by the technique of Lagrangian multipliers in structural mechanics and analyzes the nonlinear statically indeterminate structures. It is assumed that the stress-strain relationship of the materials of structures has the form of namely, the physical equations of structures have the shape of exponential functions. Several examples are given to illustrate the statically indeterminate structures such as the trusses, beams, frames and torsional bars.展开更多
文摘For statically indeterminate structure, the internal force will be changed with the translation of the supports, because the internal force is related to the absolute value of the stiffness EI. When the tension is different with the compression modulus, EI is the function of internal force and is not constant any more that is different from classic mechanics. In the other words, it is a nonlinear problem to calculate the internal force. The expression for neutral axis of the statically indeterminate structure was derived in the paper. The iterative program for nonlinear internal force was compiled. One case study was presented to illustrate the difference between the results using the different modulus theory and the single modulus theory as in classical mechanics. Finally, some reasonable suggestions were made for the different modulus structures.
文摘The paper presents the principles of a method, which in two simple stages makes possible to carry out the statically calculation of values of forces acting in the fiat static indeterminate trusses. In each stage, it is considered the static determinate truss, scheme of which is obtained after remove the suitable number of members from the basic static indeterminate truss. The both intermediate statically determinate trusses are of the same clear span and they are loaded by forces of half values applied to the corresponding truss nodes. The method applies one of the typical procedures of calculation of the statically determinate trusses and then it is applied in an appropriate way the rule of superposition for obtaining the final values of forces acting in particular members of the basic truss. The values of forces calculated in this way are of a very close approximation to the force values determined in the special and complex ways being considered as the exact calculation methods. The proposed method can be useful mostly but not only for the initial structural design of such systems. The simplicity of the two-stage method justifies an assumption that it can be relatively easy and worthy to adjust to the requirements of the computer aided technology of statically calculation of the complex forms of trusses.
基金funded by the National Natural Science Foundation of China under Grants 61873133,and 52005270in part by the Natural Science Foundation of Tianjin under Grant 21JCZDJC00090.
文摘Statically indeterminate symmetric(SIS)flexure structures are symmetric structures with“clamped-clamped”boundary conditions.The static indeterminacy and topological symmetry significantly attenuate the parasitic motions associated with statically determinate flexure structures.Hence,SIS flexure structures feature decoupled linear and angular motions,improved motion accuracy,high stiffness,and high stability.Although SIS flexure structures have been more frequently utilized as prismatic joints,they can also be utilized as revolute joints.This study systematically investigates the characteristics of SIS flexure structures.Based on the unified compliance models of a single flexure hinge,analytical compliance models of two fundamental types of SIS flexure structures are established.In 1-degree-of-freedom or planar applications,multiple SIS-based structures can also be integrated into various configurations to transmit linear or angular motions.Corresponding stiffness models are also established.The characteristics and possible applications of the SIS flexure structures are computationally investigated through case studies.Ultimately,several SIS prototypes are manufactured,and the modeling accuracy of the established stiffness models is experimentally verified.
基金Supported by National Natural Science Foundation of China(Grant Nos.61403214,61327802,U1613220)Tianjin Provincial Natural Science Foundation of China(Grant Nos.14JCZDJC31800,14JCQNJC04700)
文摘Flexure-based mechanisms are widely utilized in nano manipulations. The closed-form statics and dynamics modeling is difficult due to the complex topologies, the inevitable compliance of levers, the Hertzian contact interface, etc. This paper presents the closed-form modeling of an XY nano-manipulator consisting of statically indeterminate symmetric(SIS) structures using leaf and circular flexure hinges. Theoretical analysis reveals that the lever’s compliance, the contact stiffness, and the load mass have significant influence on the static and dynamic performances of the system.Experiments are conducted to verify the effectiveness of the established models. If no piezoelectric actuator(PEA) is installed, the influence of the contact stiffness can be eliminated. Experimental results show that the estimation error on the output stiffness and first natural frequency can reach 2% and 1.7%, respectively. If PEAs are installed, the contact stiffness shows up in the models. As no effective method is currently available to measure or estimate the contact stiffness, it is impossible to precisely estimate the performance of the overall system. In this case, the established closed-form models can be utilized to calculate the bounds of the performance. The established closed-form models are widely applicable in the design and optimization of planar flexure-based mechanisms.
文摘The paper presents general description of combined structural system and initial analysis of an innovative system proposed as the main support structure for tall or heavy loaded buildings located on subsoil of very small load-carrying ability or in earthquake areas. Moreover there is presented also an innovative two-stage method of the approximate calculation of the statically indeterminate trusses. Both are invented by the author by application of the principles of the superposition method.
文摘This paper discusses the generalized variational principles founded by the technique of Lagrangian multipliers in structural mechanics and analyzes the nonlinear statically indeterminate structures. It is assumed that the stress-strain relationship of the materials of structures has the form of namely, the physical equations of structures have the shape of exponential functions. Several examples are given to illustrate the statically indeterminate structures such as the trusses, beams, frames and torsional bars.
