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The structural analysis for crashworthiness, presented in this paper, consists of three parts: thin-walled element modeling, stiffness formulation and numerical solution. In thin-walled elements the stresses rarely reach the yield level and the element's force-deformation relationship is usually controlled by local buckling and subsequent collapse of the section. This relationship can be generally divided into four regimes: linear, post-buckling, crippling and deep collapse. In the post buckling regime only a part of the section contributes to its load carrying capacity and it is this effective part that is being used to calculate the section properties. In the deep collapse regime the stiffness is calculated by considering an appropriate mechanism of section collapse. The element stiffness is then assembled into the structural stiffness matrix. A finite element computer program is developed, incorporating this concept, for the crash simulation of general 3-dimensional structures.

A need exists for a reliable and economical analytical aid for designing vehicle structures for controlled crash energy management. Several of the crash simulation methods, currently available to the designer in the evaluation and development of vehicle structures for crash, are reviewed with respect to their capabilities and shortcomings as design aids. An analytical technique is presented, structured along the lines of a design aid and based on a finite element beam model concept. The functions of the various elements of the code are discussed in the context of typical crash events one needs to consider in the design of a structure composed of beam- and column-type elements. The heart of the proposed system code VRUSH is a component code SECOLLAPSE which monitors and predicts crush responses of thin wall structural components and which controls the input into the system code. Also presented are models generated by SECOIXAPSE for typical loading cases.

In order to understand the crush behavior of complex structural system such as a vehicle, one must first acquire the knowledge of crush characteristics of structural components that constitute the system and control its crush performance. In this paper, the crush strength characteristics and modes of collapse of thin walled circular columns are mathematically formulated. The formulation is based on the stability of shell structure subjected to axial crush, where various stages of collapse are identified and crush characteristics pertinent to column design are quantified. The effect of column size and the material properties on the collapse stability and crush strength characteristics of thin walled shell components are discussed. The size and number of folds for the axisymmetric “ring” mode and the nonsymmetric “diamond” mode are determined.

The problem of determining the theoretical load capacity or strength limits of a thin wall, axially compressed column is mathematically complex. Local instability phenomena that precede structural collapse and. the mechanism of collapse add to the complexity. In this paper, a semi-empirical approach is considered in developing design aids for sheet metal box column subjected to axial crush. Various stages of collapse are identified and crush characteristics pertinent to column design are quantified. Both are related to section geometry, column length and the material properties. The size of wave length (fold) is determined and its influence on the folding behavior of rectangular column is discussed. Design equations and charts for sizing thin wall structural elements for crush are presented. Those design aids can be implemented into finite element beam-column codes for study of crash behavior of structural systems.