Flexural rigidity

About: Flexural rigidity is a research topic. Over the lifetime, 3829 publications have been published within this topic receiving 56780 citations.

A new analytical solution estimating the flexural rigidity in the Central Andes

Abstract: SUMMARY We present a new 2-D analytical solution of the fourth-order differential equation, which describes the flexure of a thin elastic plate. The new analytical solution allows the differential equation for an elastic plate to be solved for any irregular shaped topography with a high spatial resolution. We apply the new method to the Central Andes. The flexural rigidity distribution calculated by this technique correlates well with tectonic units and the location of fault zones, for example, the Central Andean Gravity High correlates with the presence of a rigid, high-density body.

Flexural Vibrations of Elastic Sandwich Plates

Abstract: The new flexural thecny of elastic sandwich plates developed in two recent papers2 includes the effects of transverse shear deformations, rotatory and translatory inertias, and flexural and extensional rigidities, with no limitations imposed upon the magnitudes of the ratios between the thicknesses, material densities, and elastic constants of the core and faces. On the basis of the new sandwich plate theory and the exact elasticity theory, flexural vibrations of sandwich plates are investigated in this paper. Numerical results yielded by the two theories show excellent agreement with each other, and the new sandwich plate theory is seen to b^ good for a very wide frequency range that is of practical interest. The importance of the various effects involved in the theory is assessed.

Analysis of flexible bending behavior of woven preform using non-orthogonal constitutive equation

Abstract: Previous studies by Yu et al. [Yu WR, Pourboghrat F, Chung K, Zampaloni M, Kang TJ. Non-orthogonal constitutive equation for woven fabric reinforced composites. Composites Part A 2002;33:1095–1105; Yu WR, Zampaloni M, Pourboghrat F, Chung K, Kang TJ. Sheet hydroforming of woven FRT composites: non-orthogonal constitutive equation considering shear stiffness and undulation of woven structure. Compos Struct 2003;61:353–62; Yu WR, Zampaloni M, Pourboghrat F, Liu L, Chen J, Chung K, Kang TJ. Sheet forming analysis of woven FRT composites using picture-frame shear test and non-orthogonal constitutive equation. Int J Mater Prod Tech 2004;21(1/2/3):71–88] have illustrated the validity of the non-orthogonal constitutive relationship for predicting deformation behavior and changes in fiber angle in situations where woven preform was constrained by tools such as the die and blank holders. In the previous studies, the bending rigidity for out-of-plane deformation was assumed to be dependent on the in-plane stiffness; thereby the non-orthogonal constitutive equation being developed was based on the in-plane deformation geometry. The assumption for the bending rigidity was modified in this study by modeling the bending property using an asymmetric axial modulus. The asymmetric axial modulus was considered in order to utilize its ease in calculating bending rigidity from the in-plane stiffness, defining bilinear behavior over the range of tension to compression. The asymmetric factor, the ratio of compression and tensile modulus, for a woven preform was determined through simple cantilever deflection in the warp and weft directions, the validity of which was proven by conducting a cantilever deflection test and simulation in the bias direction. Finite element simulation of three-dimensional bending deformation was performed by using a non-orthogonal constitutive equation and the asymmetric axial modulus. The results show that the draped shape obtained numerically is in good agreement with the experiments in both overall deflected shape and projected contour. A shaping process was also simulated to show the usefulness of the current approach. By including the gravity and contact loading, successful prediction was made but a need was identified that extends linear asymmetric factor into nonlinear form in order to simulate large deformation in bending.

The effect of sedimentary cover on the flexural strength of continental lithosphere

Abstract: The factors that control the flexural rigidity — or effective elastic thickness (EET) — of continental lithosphere have been extensively studied over the past two decades. Using EET estimates derived from the analysis of topography, basin structures and gravity anomalies, several authors1,2,3,4,5 have shown that crustal thickness, geothermal gradient, strain rate, rheology and plate curvature all affect the flexural strength of continents. Recognition that certain combinations of these parameters result in a significant reduction of flexural strength caused by decoupling of the crust and the upper mantle3,5 has been a critical step in understanding why many continental areas have estimated EETs that are thin compared with the total mechanical thickness of the continental lithosphere5. Here we develop a semi-analytical model of the EET through a parametrization of the yield stress envelope6,7 that includes the effects of crust–mantle decoupling. We perform a detailed comparison of EET estimates at foreland basins and mountain belts to values predicted by our model and find that, to predict the EET estimates successfully, we need to take into account the effect of the sediment cover and to use a strong plagioclase-controlled rheology. The effect of sediment cover is to weaken the lithosphere because of the lower density of sediments relative to crystalline crust5,8,9 and by thermally insulating the lower crust9,10,11.