A Deformation Field for Euler–Bernoulli Beams with Applications to Flexible Multibody Dynamics

The deformation field commonly used for Euler–Bernoulli beamsin structural dynamics is investigated to determine its suitability foruse in flexible multibody dynamics. It is found that the traditionaldeformation field fails to produce an elastic rotation matrix that iscomplete to second-order in the deformation variables. A completesecond-order deformation field is proposed along with the equationsneeded to incorporate the beam model into a graph-theoretic formulationfor flexible multibody dynamics [1]. This beam modeland formulation have been implemented in a symbolic computer programcalled DynaFlex that can use Taylor, Chebyshev, or Legendrepolynomials as the basis functions in a Rayleigh–Ritz discretizationof the beam's deformation variables. To demonstrate the effects of the proposed second-order deformationfield on the response of a flexible multibody system,two examples are presented.     

Cross‐sectional shapes of the yarn in cotton gray woven fabric

This experimental work looks into the geometry of the yarn cross‐section at the weaving and relaxed stages using microscopic and digital image processing techniques. A total of 54 plain‐weave cotton fabric samples (different in the yarn twist and the fabric density) were produced and the cross‐sectional shapes of the wefts at the early stage of weaving (in which the wefts were also under tension by full‐width temples) and at the relaxed state were compared with the ideal circular shape. The measurements of the samples showed that the cross‐sectional shapes of the yarns at the early stage of weaving are circular, elliptical or a combination of two circles or an asymmetric elliptical. Moreover, the effect of the fabric tightness on the yarn cross‐sectional shape and dimension was negligible. The measurements of the cross‐sectional dimensions of the relaxed fabric (released from weaving tension) showed an increase in the area occupied by the yarn inside the fabric and did not follow the Peirce standard model. The measurement and the comparison showed that the cross‐sections of the yarns inside the woven fabric could be categorized into five different shapes, namely; circular (C), elliptical (E), sharp symmetrical amygdaloidal (SSA), asymmetrical amygdaloidal (AA) and sharp asymmetrical amygdaloidal (SAA), but the number of each group depends upon the yarn properties and the fabric structures. The fabrics with the highest density and the highest twisted yarns had a circular cross‐sectional shape, whereas the fabrics with the lowest fabric density and the lowest twisted yarns had the most flattened yarn cross‐sections in the form of sharp symmetrical or asymmetrical amygdaloidal shapes.     

Theory of micropolar gyroelastic continua

This paper is devoted to the dynamic modeling of micropolar gyroelastic continua and explores some of the modeling and analysis issues related to them. It can be considered as an extension of the previous studies on equivalent continuum modeling of truss structures with or without angular momentum devices. Assuming unrestricted or large attitude changes for the axes of the gyros and utilizing the micropolar theory of elasticity, the energy expressions and equations of motion for undamped micropolar gyroelastic continua are derived. Whereas the micropolar gyroelastic continuum model with extra coefficients and degrees of freedom is primarily developed to account for the asymmetric stress–strain analysis in the gyroelastic continua, it also proves to be beneficial for a more comprehensive representation of the actual gyroelastic structure. The dynamic equations of the general gyroelastic continua are reduced to the case of one-dimensional gyroelastic beams. Simplified micropolar beam torsion and bending theories are used to derive the governing dynamic equations of micropolar gyroelastic beams from Hamilton’s principle. A finite element model corresponding to the micropolar gyrobeams is built in MATLAB\({^{\circledR}}\) and is used in numerical examples to study the spectral and modal behavior of simply supported micropolar gyroelastic beams.     

Mixed mode fracture analysis of rectilinear anisotropic plates by high order finite elements

A singular finite element is developed for direct calculation of combined modes I and II stress intensity factors for planar rectilinear anisotropic structures subject to arbitrary loading. Twelve-node conventional elements are used in conjunction with a linear elastic fracture mechanics enrichment of the same element which is formed into a four-element macro-element. Example problems show this formulation to be exceptionally accurate and results are presented for a variety of modern fibre-reinforced composites in simple mode I extension and in mixed mode I and II situations. In addition, it is shown that the meshes for accurate results are relatively coarse and thus calculations are quite economical.     

A linear coupling controller for plate vibration

A means of designing linear coupling controllers for multi-degree-of-freedom systems is developed and applied to a thin plate partially clamped on one edge and free on all other edges. The linear-coupling controller developed here is compared to other controllers. Both simulated and experimental results show that the design algorithm presented here provides control over a wider frequency range.     

The influence of forcing conforming boundaries on a high precision enriched fracture element

The influence of forcing a non-conforming enriched element to be conforming by way of zeroing functions is investigated. The element under consideration is a twelve-node rectangular element which was developed previously for the calculation of mode I and II stress intensity factors for rectilinear anisotropic planar materials. Three different types of zeroing functions are considered. It is demonstrated that the accuracy of the resulting conforming elements depends on the shape of the zeroing function used but still yields unacceptable results for finite element grids where the non-conforming element yields extremely accurate results.