R. Stocki

Reliability assessment for sheet metal forming operations

Methodology developed for reliability calculations of structures is applied to estimate reliability of sheet metal forming operations. Sheet forming operations are one of the most common technological processes but still the tool and process design is a difficult engineering problem. Product defects are often encountered in the industrial practice. Material breakage, wrinkling, shape defects due to springback are most frequent defects in sheet metal forming operations. Numerical simulation allows us to evaluate product manufacturability and predict the defects at early stages of the design process. In the paper the so-called forming limit diagrams (FLD) are used as a criterion of material breakage in the manufacturing process. A zone of a FLD where good results are guaranteed with sufficient probability is considered as safe zone. Sheet forming operations are characterized with a significant scatter of the results. This can be caused by differences that can occur in forming of each part. Small differences in the contact conditions, for instance, can lead to significant changes in the deformation state of the sheet. In reliability-like approach we try to quantify intuitive terms of probability of failure/success of forming operations given some uncertainty of parameters characterizing a forming process like friction parameters or blankholding force. Since the employment of the gradient-based reliability techniques is very much limited due to the some degree of numerical noise introduced by the explicit dynamic algorithm used to perform sheet stamping simulation the method of adaptive Monte Carlo simulations were chosen for reliability assessment.

Study on discrete optimization techniques in reliability-based optimization of truss structures

Abstract The paper deals with application of two optimization techniques to solve mixed (discrete–continuous) reliability-based optimization (RBO) problem of truss structures. The mixed RBO problem is formulated as the minimization of structural volume subjected to the constraints on the values of componental reliability indices determined by FORM approach. The cross-sectional areas of truss bars and coordinates of the specified truss nodes are considered as discrete and continuous design variables, respectively. The specified allowable reliability indices are associated with limit states in the form of the admissible displacements of the chosen truss nodes, admissible stress or local buckling of the elements as well as a global loss of stability. Two optimization techniques, namely: transformation and controlled enumeration methods are employed to solve the optimization problem. The transformation method allows to transform the mixed optimization problem into the continuous one. Two numerical examples: 10 bar planar truss and spatial truss dome are used to illustrate the proposed methodology of solution. Results obtained by both methods are compared and appropriate conclusions are drawn.

Reliability analysis of a crashed thin-walled s-rail accounting for random spot weld failures

Possibly the most common application of spot welding is in the automobile manufacturing industry, where it is almost universally used to weld the sheet-metal car components. However, due to manufacturing inaccuracies and fatigue failures an important number of spot welds may be missing in an operational vehicle. It seems that to properly analyse the reliability of such structures, in particular crashworthiness reliability, the spot weld failures must be considered. Representing properties of each spot weld in a stochastic model by corresponding random variables is extremely inefficient. Therefore, in this article an approach is proposed for handling spot-weld defects in the reliability analysis by accounting for their averaged influence on a failure criterion. The approach consists of the appropriate treatment of a random noise component of the limit state function. The noise results from the strategy of deleting a certain number of randomly selected spot-weld elements from the finite element model each time the limit state function value is computed. Dealing with noisy limit state functions in structural reliability analysis is a challenging task. The only method that seems to be insensitive to this phenomenon is Monte Carlo sampling, which for most of the applications of practical interest is prohibitively expensive. Having this in mind, a method based on the algorithm proposed by Zou et al. and published in the journal of Reliability Engineering and System Safety in 2002 is investigated in this article. The method combines the best features of the first-order reliability method, the response surface technique and the importance sampling method to achieve both accuracy and efficiency. A detailed study on the reliability of thin-walled s-rail subjected to crash is performed. Some suggestions concerning the modification of the original algorithm are proposed.

Reliability-Based Analysis of Large Deformations in Metal Forming Operations

Methodology developed for reliability calculations of structures is applied to estimate reliability of sheet metal forming operations, typical mechanical problems characterized with large deformations. Forming Limit Diagrams (FLD) used in the industrial practice as a criterion of material breakage in the manufacturing process are treated as the limit state function for reliability analysis. We try to quantify intuitive terms of probability of failure/success of forming operations given some uncertainty of parameters characterizing a forming process like friction parameters or blankholding force. Since the employment of the gradient-based reliability techniques is very much limited due to numerical noise introduced by the explicit dynamic algorithm used to perform sheet stamping simulation, the method of Adaptive Monte Carlo simulations and Response Surface method were chosen for reliability assessment.