Infinitesimal-rotation finite elements allow creating a linear problem that can be exploited to systematically reduce the number of coordinates and obtain efficient solutions for a wide range of applications,including...Infinitesimal-rotation finite elements allow creating a linear problem that can be exploited to systematically reduce the number of coordinates and obtain efficient solutions for a wide range of applications,including those governed by nonlinear equations.This paper discusses the limitations of conventional infinitesimal-rotation finite elements(FE)in capturing correctly the initial stress-free reference-configuration geometry,and explains the effect of these limitations on the definition of the inertia used in the motion description.An alternative to conventional infinitesimal-rotation finite elements is a new class of elements that allow developing inertia expressions written explicitly in terms of constant coefficients that define accurately the reference-configuration geometry.It is shown that using a geometrically inconsistent(GI)approach that introduces the infinitesimal-rotation coordinates from the outset to replace the interpolation-polynomial coefficients is the main source of the failure to capture correctly the reference-configuration geometry.On the other hand,by using a geometrically consistent(GC)approach that employs the position gradients of the absolute nodal coordinate formulation(ANCF)to define the infinitesimal-rotation coordinates,the reference-configuration geometry can be preserved.Two simple examples of straight and tapered beams are used to demonstrate the basic differences between the two fundamentally different approaches used to introduce the infinitesimal-rotation coordinates.The analysis presented in this study sheds light on the differences between the incremental co-rotational solution procedure,widely used in computational structural mechanics,and the non-incremental floating frame of reference formulation(FFR),widely used in multibody system(MBS)dynamics.展开更多
The concept of a space solar power station(SSPS)was proposed in 1968 as a potential approach for solving the energy crisis.In the past 50 years,several structural concepts have been proposed,but none have been sent in...The concept of a space solar power station(SSPS)was proposed in 1968 as a potential approach for solving the energy crisis.In the past 50 years,several structural concepts have been proposed,but none have been sent into orbit.One of the main challenges of the SSPS is dynamic behavior prediction,which can supply the necessary information for control strategy design.The ultra-large size of the SSPS causes difficulties in its dynamic analysis,such as the ultra-low vibration frequency and large fexibility.In this paper,four approaches for the numerical analysis of the dynamic problems associated with the SSPS are reviewed:the finite element,absolute nodal coordinate,foating frame formulation,and structure-preserving methods.Both the merits and shortcomings of the above four approaches are introduced when they are employed in dynamic problems associated with the SSPS.Synthesizing the merits of the aforementioned four approaches,we believe that embedding the structure-preserving method into finite element software may be an effective way to perform a numerical analysis of the dynamic problems associated with the SSPS.展开更多
基金supported,in part,by the National Science Foundation(Grant 1852510).
文摘Infinitesimal-rotation finite elements allow creating a linear problem that can be exploited to systematically reduce the number of coordinates and obtain efficient solutions for a wide range of applications,including those governed by nonlinear equations.This paper discusses the limitations of conventional infinitesimal-rotation finite elements(FE)in capturing correctly the initial stress-free reference-configuration geometry,and explains the effect of these limitations on the definition of the inertia used in the motion description.An alternative to conventional infinitesimal-rotation finite elements is a new class of elements that allow developing inertia expressions written explicitly in terms of constant coefficients that define accurately the reference-configuration geometry.It is shown that using a geometrically inconsistent(GI)approach that introduces the infinitesimal-rotation coordinates from the outset to replace the interpolation-polynomial coefficients is the main source of the failure to capture correctly the reference-configuration geometry.On the other hand,by using a geometrically consistent(GC)approach that employs the position gradients of the absolute nodal coordinate formulation(ANCF)to define the infinitesimal-rotation coordinates,the reference-configuration geometry can be preserved.Two simple examples of straight and tapered beams are used to demonstrate the basic differences between the two fundamentally different approaches used to introduce the infinitesimal-rotation coordinates.The analysis presented in this study sheds light on the differences between the incremental co-rotational solution procedure,widely used in computational structural mechanics,and the non-incremental floating frame of reference formulation(FFR),widely used in multibody system(MBS)dynamics.
基金supported by the National Natural Science Foundation of China(12172281,11972284,11672241,11432010,and 11872303)Fund for Distinguished Young Scholars of Shaanxi Province(2019JC-29)+2 种基金Foundation Strengthening Program Technical Area Fund(2021-JCJQ-JJ-0565)Fund of the Science and Technology Innovation Team of Shaanxi(2022TD-61)Fund of the Youth Innovation Team of Shaanxi Universities.
文摘The concept of a space solar power station(SSPS)was proposed in 1968 as a potential approach for solving the energy crisis.In the past 50 years,several structural concepts have been proposed,but none have been sent into orbit.One of the main challenges of the SSPS is dynamic behavior prediction,which can supply the necessary information for control strategy design.The ultra-large size of the SSPS causes difficulties in its dynamic analysis,such as the ultra-low vibration frequency and large fexibility.In this paper,four approaches for the numerical analysis of the dynamic problems associated with the SSPS are reviewed:the finite element,absolute nodal coordinate,foating frame formulation,and structure-preserving methods.Both the merits and shortcomings of the above four approaches are introduced when they are employed in dynamic problems associated with the SSPS.Synthesizing the merits of the aforementioned four approaches,we believe that embedding the structure-preserving method into finite element software may be an effective way to perform a numerical analysis of the dynamic problems associated with the SSPS.
