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
Understanding solid‐and fluid‐inertia forces and their coupling with the gravity potential in complex motion scenarios is necessary for evaluating system stability and identifying root causes of system failure and a...Understanding solid‐and fluid‐inertia forces and their coupling with the gravity potential in complex motion scenarios is necessary for evaluating system stability and identifying root causes of system failure and accidents.Because solids and fluids have an infinite number of degrees of freedom and distributed inertia and elasticity,having meaningful qualitative and quantitative nominal measures of the kinematics and forces will contribute to a better understanding of the system dynamics.This paper proposes developing new continuum‐based nominal measures for the characterization of the oscillations and forces.By using a material‐point approach,these new nominal measures,which have their roots in the continuum‐mechanics partial‐differential equations of equilibrium and Frenet geometry,are independent of the formulation or generalized coordinates used to develop the dynamic equations of motion.The paper proposes a data‐driven‐science approach to define a nominal continuum space‐curve geometry with nominal curvature and torsion;a nominal instantaneous motion plane(IMP),which contains the resultant of all forces including the inertia forces;and a nominal instantaneous zero‐force axis(IZFA)along which the resultant of all forces vanishes.While using the material‐point approach eliminates the need for introducing moment equations associated with orientation coordinates,the IMP and IZFA concepts can be used to define the instantaneous axis of significant moment components,which can lead to accidents such as in the case of vehicle rollovers.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.
文摘Understanding solid‐and fluid‐inertia forces and their coupling with the gravity potential in complex motion scenarios is necessary for evaluating system stability and identifying root causes of system failure and accidents.Because solids and fluids have an infinite number of degrees of freedom and distributed inertia and elasticity,having meaningful qualitative and quantitative nominal measures of the kinematics and forces will contribute to a better understanding of the system dynamics.This paper proposes developing new continuum‐based nominal measures for the characterization of the oscillations and forces.By using a material‐point approach,these new nominal measures,which have their roots in the continuum‐mechanics partial‐differential equations of equilibrium and Frenet geometry,are independent of the formulation or generalized coordinates used to develop the dynamic equations of motion.The paper proposes a data‐driven‐science approach to define a nominal continuum space‐curve geometry with nominal curvature and torsion;a nominal instantaneous motion plane(IMP),which contains the resultant of all forces including the inertia forces;and a nominal instantaneous zero‐force axis(IZFA)along which the resultant of all forces vanishes.While using the material‐point approach eliminates the need for introducing moment equations associated with orientation coordinates,the IMP and IZFA concepts can be used to define the instantaneous axis of significant moment components,which can lead to accidents such as in the case of vehicle rollovers.
