Vehicle Mass, Stiffness and Their Relationship
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Vehicle stiffness is a commonly used parameter in the field of vehicle safety. But a single-valued “stiffness”, although well defined for the linear case, is not well defined for non-linear systems, such as vehicle crashes. Moreover, the relationship between vehicle stiffness and mass remains confusing. One previous work [Vehicle Mass and Stiffness: Search for a Relationship, G. Nusholtz, SAE2004, 04CONG--17, 2004 SAE International Congress, March, Detroit, USA, 2004] addresses this issue. Multiple definitions of stiffness were used to address the lack of a clear definition of stiffness. The R-squared values for the correlation between mass and each stiffness measure were presented. The results showed that no clear relationship existed between mass and any of the stiffness measures. The results from a statistical analysis indicated that there were differences in stiffness between different types of vehicles. This paper extends the same research by including a significant amount of new data samples as well as some different analysis procedures. Results show that mass is poorly correlated to stiffness and for some vehicle types mass correlates better to vehicle crush than to stiffness. In addition, it is shown that even without a well-defined definition of stiffness different levels of stiffness can be defined and differences in stiffness between different vehicle types can be quantitatively and qualitatively established.Keywords:
Direct stiffness method
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This paper is concerned with the reanalysis of structures with local stiffness changes. The problem arises in finite element analysis of structures with some damaged components or yielding elements. A new algorithm is presented in which the reanalysis of the complete new structure is rendered unnecessary. An exact result is obtained with some algebraic manipulation of the LDLT factors of the original stiffness matrix. The computational time is same as that consumed in other methods. In addition, the present method is general. It is applicable to any type of structure, such as bar抯 structure system or continuum problem. Numerical examples are provided, showing that the new algorithm is effective in calculating structures with local stiffness changes.
Direct stiffness method
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The work is to present the energetic nature of the rigidity. It starts with the definition by introducing the notion of sensual magnitudes with the pyramidal structure of all surrounding magnitudes known by a human being. Next the selection of the subject is provided in view of a smooth categorization of magnitudes describing the reality. The adequate description of the considered mechanical phenomenon is presented by formulating general stiffness characteristics. There are several characteristics analyzed, both functional and parametric. An essential, quite a new one is the characteristic of stiffness energy measure which is the stiffness potential. The proper and gained stiffness potentials situated on stable and unstable potential fields have been analyzed. An example of using of this theory to practice is given. It has been referred to a cylindrical grinder case. The presented theory allowed describing the entire stiffness characteristics, including its initial very essential course which has been usually, though inequitably, extrapolated by a straight line segment coming out of zero point with zero coordinates.
Rigidity (electromagnetism)
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Pipe supports are represented as spring constants in piping analysis, and therefore a formal procedure is required to determine the spring constant values. Two current approaches are to enforce deflection criteria to ensure support rigidity or calculate the support stiffness values directly. However, the former approach results in overly conservative support designs and the latter approach becomes an iterative process of designing the supports and observing the response of the piping system. To avoid the issues presented by these methods, an alternative approach is presented which involves increasing values of support stiffness until change in natural frequency of the system diminishes. This method can help establish a lower bound (minimum rigid) stiffness above which there will be no significant change in the seismic response of the piping system. Using this approach only requires the support designs to have stiffness values at or above the minimum value without being concerned with detailed stiffness calculations or using deflection limits. This paper presents the methods and results of an expansive study to establish minimum rigid stiffness values for piping analysis.
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This paper studied the reanalyzes method of the structure when stiffness changed in local area.The problem often arrived when finite element analyses for the structure with a few components damaged or some elements yield,etc.In this paper,a new solution algorithm is derived,which used the LDLT factors of the stiffness matrix of the old structure with some algebraically calculating.It need not reanalyze the whole new structure,but the result is exact.It takes the same calculation time as the methods that presented in other literature.In addition,the method preaented in this paper is general.It can be used to analyses any type of structure,example,bar's structure system or contimuum problem.The example in this paper shows that the new algorithm is effective in calculating the structure with local stiffness changed.
Direct stiffness method
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The Automotive Composites Consortium has initiated the third of a series of focal projects, which is a multiyear program to develop a design and manufacturing strategy for a composite intensive body-in-white (BIW) with aggressive mass reduction, manufacturing cycle time, and cost parity targets. Specifically, the BIW is to exhibit 60% minimum mass savings over the conventional steel baseline, contain the same package space as the baseline, meet or exceed the structural performance, and have cost parity to the baseline in volumes exceeding 100,000 per annum. The Department of Energy’s Office of Advanced Automotive Technology provided most of the funding for this project. A design study was undertaken to evaluate whether the mass savings are feasible – utilizing carbon-fiber composites – without sacrificing structural performance. The design was conducted with consideration to costeffective composites manufacturing processes that are under development. This paper will present objectives of this focused program, results of the design study, and a discussion of the technical challenges that will be addressed during the remainder of the program.
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It has previously been done analyses to find global stiffness values of an umbilical cable, with mixed results or no results at all when subjected to bending. There have also been difficulties in finding a distinct stick-slip point during bending. In this thesis, several models have been examined to get a step closer to resolve these particular issues. To begin with, a very simple flexible cable has been tested to see if the program ANSYS LS-Dyna can provide good global stiffness values, then of course with the use of an explicit scheme. When this first analysis gave good results, it was possible to conclude that the program could handle analyzing long slender structures with good accuracy. Further it was also developed a model with the aim of predicting the stick-slip phenomenon during bending. Results from this model could imply that there existed a stick-slip point, only a short time after the bending started. Finally, a last model was developed, including two armour layers wound around a cover of polyethylene. Other analyses have had problems with the behavior of the tendons during bending, that is they have been spreading, and not been following a loxodromic curve. Different cable lengths were tested, showing relative good results for the axial- and bending stiffness, but not so good results for the torsional stiffness. In addition to be able to develop models that could give realistic global stiffness values, focus have been on reducing the CPU time as much as possible. Therefore, much time has been spent on modeling the models right, and choosing the right path and length of loading.
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The empirical formulae formulated in history for calculation of rolling bearing stiffness do not show how to predict the accuracy of dependant variables from the accuracy of independant variables or to what extent the stiffness is reliable. The magnitude of errors will be widened as the independent variables move away from the average mean values of experimental data, for instance, there will be larger errors for stiffness obtained using the empirical formulae for a small or large load. These are very important for statistic treatment of modern experimental data. Theoretical formulae have been derived by following the linear elasticity theory for calculation of aerospace rolling bearing stiffness, and the stiffness of three kinds of aerospace bearings are calculated using theoretical and empirical formulae respectively for a particular load, and there is a good agreement between the results. The scope of applicability for independant variables, such as loads, in the theoretical formulae based upon the linear elasticity theory is much wider than that in the empirical formulae. The errors for the calculated stiffness in the theoretical formulae can be directly obtained from the errors for the independant variables, and theoretical formulae should be used for more accurate calculcation or selection of bearings.
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