Mitsuo Iwahara

Structural optimum design using pseudo-least-squares method—part I.: extension to inequality behavior constraints

Abstract This paper discusses an application of the pseudo-least-squares method to dynamic optimization, with a theoretical extension to inequality behaviour constraints. The application is to a large-scale model, with as many as 8259 degrees of freedom and 1508 design variables. The large-scale model is an engine cylinder block model which has been chosen from the improvement of its torsional resonant frequency. The necessary calculations were completed in eight repetition cycles in the case of a combination of equality and inequality behaviour constraints. The CPU time used for optimization was 0.05 minutes, while the CPU times for eigenvalue analysis and sensitivity analysis were 6.4 and 3.4 minutes, respectively. The results revealed some new information, which we used to manufacture a prototype of an engine block on the basis of the final calculation model. The test result proved quite satisfactory.

An Investigation of the Small Crack and Structural Modification for a Big Impeller

The crack arose during actual operation, in an impeller of large-sized blower, at the joint part of the main board and blade. For the purpose to clarify, this phenomenon, dynamic analysis and static analysis using the finite element method were performed. The analysis results showed that the cause of a crack of impeller is the stress which occurs owing to the deformation of the side board by centrifugal force. This deformation is wave like one which is same pitch as blade. Then, the structural modification by pseudo-inverse method was performed for the purpose of stress reduction. In this case, designer does not want the minimum weight optimum design but the minimum modification design. Pseudo-inverse method may modify the structure with the minimum distance in the design variable space to satisfy the stress restriction. Some cases are tried. When the design variables were 3 main parts thicknesses, those are main board, side board and blade, practical solution is deduced for 8 calculations to satisfy the stress limit with 10% weight increase.

An Optimization Method with Pseudo-Least-Squares Method.

This method is proposed for a FEM model which has a large number of elements. This minimizes the length of the modification vector in design variable space. In this paper, an expansion is introduced to satisfy unequal behaviour constraints and side constraints. Also, a new approach searching for the minimum norm of design variables is added. The calculations with a small model elucidate the effectiveness of this theory.

Classification of Vibration Modes and Optimization of Vibration Characteristics of a Simplified Cylinder Block Model.

An engine cylinder block usually has complex mode shapes. When designing an engine, engineers try to achieve what they think is the best on the basis of their judgement. However they must consider a great variety of modes. In this research, a very simplified 4-cylinder block model has been developed. (1) to classify basic modes both qualitatively and quantitatively, (2) to predict the change in natural frequencies in neighborhood of the target with the optimization method, and (3) to optimize the natural frequency of this model using the techniques of the pseudo-inverse method. It has been found that the similarity between the vectors of natural frequency sensitivity has significant effects on mode-to-mode variations in natural frequency.

Structural optimum design using pseudo-least-squares method—part II.: application to car body design

Abstract This paper discusses an application of the minimum-norm pseudo-least-squares Method to the design of an open-body car. A side constraint is provided to avoid a loop in the calculation, and the dynamic target and static target are considered simultaneously. In the case of removing the roof of a monocoque car body in a simple manner, the bending resonant frequency and the torsional rigidity were decreased drastically, to one-third and one-eighth, respectively. In order to counter this decrease, the optimum design method is applied here; the design variables are the thicknesses of all the shell elements (2863 in all). Calculation of the optimum design, and manual designing of reinforcement on the basis of the results of that calculation, have been repeated. Finally, we achieved a calculation model which satisfies the requirements.