Energy-minimizing inclusion in an elastic plate under remote shear

Vigdergauz, Shmuel

doi:10.2140/jomms.2008.3.63

Cited by 4 publications

(2 citation statements)

References 14 publications

(18 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the present article a rigid inclusion or a void is analyzed with a hypocycloidal shape of order n embedded in an elastic-isotropic plane subject to a remote loading condition of nonuniform antiplane shear represented as a polynomial of order m. For Published in Journal of Elasticity 126, 215-229 (2017) doi: http://dx.doi.org/10.1007/s10659-016-9590-5 uniform remote load (m = 0), this problem has been thoroughly investigated, for both the cases of rigid inclusions and voids, when plane [6,7,9,10,14,15,25,30,31,32] or antiplane [26,27,39,40] conditions prevail; a case of nonlinear elastic behaviour has also been recently considered [41]. However, the disuniformity in the applied load (m = 0), analyzed here for the first time, yields unexpected and counter intuitive results, which are important to understand the complexity arising form the highly-varying fields that can develop in composite materials deformed in extreme conditions.…”

Section: Introductionmentioning

confidence: 99%

Hypocycloidal Inclusions in Nonuniform Out-of-Plane Elasticity: Stress Singularity vs. Stress Reduction

Shahzad

Corso

Bigoni

2016

J Elast

View full text Add to dashboard Cite

Stress field solutions and Stress Intensity Factors (SIFs) are found for n-cusped hypocycloidal shaped voids and rigid inclusions in an infinite linear elastic plane subject to nonuniform remote antiplane loading, using complex potential and conformal mapping. It is shown that a void with hypocycloidal shape can lead to a higher SIF than that induced by a corresponding star-shaped crack; this is counter intuitive as the latter usually produces a more severe stress field in the material. Moreover, it is observed that when the order m of the polynomial governing the remote loading grows, the stress fields generated by the hypocycloidal-shaped void and the star-shaped crack tend to coincide, so that they become equivalent from the point of view of a failure analysis. Finally, special geometries and loading conditions are discovered for which there is no stress singularity at the inclusion cusps and where the stress is even reduced with respect to the case of the absence of the inclusion. The concept of Stress Reduction Factor (SRF) in the presence of a sharp wedge is therefore introduced, contrasting with the well-known definition of Stress Concentration Factor (SCF) in the presence of inclusions with smooth boundary. The results presented in this paper provide criteria that will help in the design of ultra strong composite materials, where stress singularities always promote failure. Furthermore, they will facilitate finding the special conditions where resistance can be optimized in the presence of inclusions with non-smooth boundary.

show abstract

Section: Introductionmentioning

confidence: 99%

Hypocycloidal Inclusions in Nonuniform Out-of-Plane Elasticity: Stress Singularity vs. Stress Reduction

Shahzad

Corso

Bigoni

2016

J Elast

View full text Add to dashboard Cite

show abstract

“…2 The use of BIEs restricts this scheme to problems with either linear or linearized governing equations. 3 The theory of analytic functions is also pivotal in two-dimensional shape optimization problems in fluid and structural mechanics [8,[29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Minimum-resistance shapes in linear continuum mechanics

Zabarankin

2013

Proc. R. Soc. A.

View full text Add to dashboard Cite

A necessary optimality condition for the problem of the minimum-resistance shape for a rigid threedimensional inclusion displaced in an unbounded isotropic elastic medium subject to a constraint on the volume of the inclusion is obtained through Betti's reciprocal work theorem. It generalizes Pironneau's optimality condition for the minimum-drag shape for a rigid body immersed into a uniform Stokes flow and is specialized for axisymmetric inclusions in axisymmetric and transversal translations. In both cases of translation, the three-dimensional displacement field is represented in terms of generalized analytic functions, and the three-dimensional elastostatics problem is reduced to boundary-integral equations (BIEs) via the generalized Cauchy integral formula. Minimum-resistance shapes are found in the semi-analytical form of functional series from an iterative procedure coupling the optimality condition and the BIEs. They are compared with the minimumresistance spheroids and with the minimum-resistance spindle-shaped and lens-shaped bodies. Remarkably, in the axisymmetric translation, the minimumresistance shapes transition from spindle-like shapes to almost prolate spheroidal shapes as the Poisson ratio changes from 1/2 to 0, whereas in the transversal translation, they are close to oblate spheroidal shapes for any Poisson ratio.

show abstract

Shape optimization of two interacting holes with different areas in an infinite plate

Cai

2019

European Journal of Mechanics - A/Solids

View full text Add to dashboard Cite

Energy-minimizing inclusion in an elastic plate under remote shear

Cited by 4 publications

References 14 publications

Hypocycloidal Inclusions in Nonuniform Out-of-Plane Elasticity: Stress Singularity vs. Stress Reduction

Hypocycloidal Inclusions in Nonuniform Out-of-Plane Elasticity: Stress Singularity vs. Stress Reduction

Minimum-resistance shapes in linear continuum mechanics

Shape optimization of two interacting holes with different areas in an infinite plate

Contact Info

Product

Resources

About