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Frames are important structures found in many transportation applications such as automotive bodies and train cars. They are also widely employed in buildings, bridges, and other load bearing designs. When a frame is carrying multiple loads, it can potentially risk a catastrophic buckling failure. The loads on the frame may be non-proportional in that one force stays constant while the other is increased until buckling occurs. In this study the buckling problem is formulated as a constrained eigenvalue problem (CEVP). As opposed to other CEVP in which the eigenvectors are forced to comply with a number of the constraints, the eigenvalues in the current CEVP are subject to some equality constraints. A numerical algorithm for solving the constrained eigenvalue problem is presented. The algorithm is a simple trapping scheme in which the computation starts with an initial guess and a window containing the potential target for the eigenvalue is identified.

In today's light-weight vehicles, the strength of spot welds plays an important role in overall product integrity, reliability and customer satisfaction. Naturally, there is a need for a quick and reliable technique to inspect the quality of the welds. In the past, the primary quality control tests for detecting weld defects are the destructive chisel test and peel test [1]. The non-destructive evaluation (NDE) method currently used in industry is based on ultrasonic inspection [2, 3, 4]. The technique is not always successful in evaluating the nugget size, nor is it effective in detecting the so-called “cold” or “stick” welds. Therefore, it is necessary to develop a precise and reliable noncontact NDE method for spot welds. There have been numerous studies in predicting the weld nugget size by considering the spot-weld process [5, 6].

Coatings have the potential to improve bearing tribological performance. However, every coating application process and material combination may create different residual stresses and coating microstructures, and their effect on bearing fatigue and wear performance is unclear. The aim of this work is to investigate coating induced residual stress effects on bearing failure indicators using a microstructural contact mechanics (MSCM) finite element (FE) model. The MSCM FE model consists of a two-dimensional FE model of a coated bearing surface under sliding contact where individual grains are represented by FE domains. Interactions between FE domains are represented using contact element pairs. Unique to this layered rolling contact FE model is the use of polycrystalline material models to represent realistic bearing and coating microstructural behavior. The MSCM FE model was compared to a second non-microstructural contact mechanics (non-MSCM) model.

To ensure ride comfort, the dynamic characteristics, such as natural frequencies, of a vehicle is often tuned to a specific value by managing the magnitude and location of some masses and/or configuration of stiffeners without sacrificing the structural strength and overall fuel performance of the vehicle. We first formulate the mathematical statement of the problem in a constrained eigenvalue form. Optimal solutions are sought using various finite element techniques. A novel methodology involving genetic algorithm and Newton’s iterative method is developed to solve the constrained eigenvalue problems. Several examples, including discrete and continuous systems, are presented to demonstrate the effectiveness and accuracy of the proposed methodology. The strategy of managing the mass location and distribution to target a preferred natural frequency or frequencies is given in the conclusion.