Uniform minimum moment aberration designs

An efficient orthogonal array was constructed with near balance and near the orthogonal property for the lowest common multiples of runs, using the balance coefficient criteria for determining near balance and J2 optimality criteria for orthogonal properties. The optimization and distance function forms of balance coefficient criteria were used for the classification of the designs. The Minimum Moment Aberration (MMA) and Minimum Aberration Projection (MAP) are compared using the optimization and distance function to determine the near balance criteria. The result indicated that, the MMA and MAP criteria was efficient using the optimization procedure of the balance coefficient.

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Stability of a Rigid Body With an Oscillating Particle: An Application of MACSYMA

Journal of Applied Mechanics ◽

10.1115/1.3169122 ◽

1985 ◽

Vol 52 (3) ◽

pp. 686-692 ◽

Cited By ~ 4

Author(s):

L. A. Month ◽

R. H. Rand

Keyword(s):

Angular Velocity ◽

Rigid Body ◽

Classical Problem ◽

Moment Of Inertia ◽

Model Parameters ◽

Stability Chart ◽

The Stability ◽

Transition Curves ◽

Minimum Moment ◽

Small Angular Velocity

This problem is a generalization of the classical problem of the stability of a spinning rigid body. We obtain the stability chart by using: (i) the computer algebra system MACSYMA in conjunction with a perturbation method, and (ii) numerical integration based on Floquet theory. We show that the form of the stability chart is different for each of the three cases in which the spin axis is the minimum, maximum, or middle principal moment of inertia axis. In particular, a rotation with arbitrarily small angular velocity about the maximum moment of inertia axis can be made unstable by appropriately choosing the model parameters. In contrast, a rotation about the minimum moment of inertia axis is always stable for a sufficiently small angular velocity. The MACSYMA program, which we used to obtain the transition curves, is included in the Appendix.

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A numerical approach to determine fiber orientations around geometric discontinuities in designing against failure of GFRP laminates

International Journal of Structural Integrity ◽

10.1108/ijsi-10-2018-0064 ◽

2019 ◽

Vol 10 (3) ◽

pp. 371-379 ◽

Cited By ~ 2

Author(s):

Roselita Fragoudakis

Keyword(s):

Stress Concentration ◽

Plastic Zone ◽

Stress Concentration Factor ◽

Concentration Factor ◽

Load Condition ◽

Content Type ◽

Geometric Discontinuities ◽

Failure Theories ◽

Laminated Structures ◽

Minimum Moment

Purpose Determining fiber orientations around geometric discontinuities is challenging and simultaneously crucial when designing laminates against failure. The purpose of this paper is to present an approach for selecting the fiber orientations in the vicinity of a geometric discontinuity; more specifically round holes with edge cracks. Maximum stresses in the discontinuity region are calculated using Classical Lamination Theory (CLT) and the stress concentration factor for the aforementioned condition. The minimum moment to cause failure in a lamina is estimated using the Tsai–Hill and Tsai–Wu failure theories for a symmetric general stacking laminate. Fiber orientations around the discontinuity are obtained using the Tsai–Hill failure theory. Design/methodology/approach The current research focuses on a general stacking sequence laminate under three-point bending conditions. The laminate material is S2 fiber glass/epoxy. The concepts of mode I stress intensity factor and plastic zone radius are applied to decide the radius of the plastic zone, and stress concentration factor that multiplies the CLT stress distribution in the vicinity of the discontinuity. The magnitude of the minimum moment to cause failure in each ply is then estimated using the Tsai–Hill and Tsai–Wu failure theories, under the aforementioned stress concentration. Findings The findings of the study are as follows: it confirms the conclusions of previous research that the size and shape of the discontinuity have a significant effect on determining such orientations; the dimensions of the laminate and laminae not only affect the CLT results, but also the effect of the discontinuity in these results; and each lamina depending on its position in the laminate will have a different minimum load to cause failure and consequently, a different fiber orientation around the geometric discontinuity. Originality/value This paper discusses an important topic for the manufacturing and design against failure of Glass Fiber Reinforced Plastic (GFRP) laminated structures. The topic of introducing geometric discontinuities in unidirectional GFRP laminates is still a challenging one. This paper addresses these issues under 3pt bending conditions, a load condition rarely approached in literature. Therefore, it presents a fairly simple approach to strengthen geometric discontinuity regions without discontinuing fibers.

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