Approximate Analytical Solution for a Unilateral Contact Problem with Heavy Elastica

Higher-order asymptotic crack-tip fields in simplified strain gradient elasticity

“…Formal derivation and proof for the completeness theorem of representation ( 13)- (15) for the isotropic Mindlin-Toupin strain gradient elasticity have been presented recently in [41]. Application of general solution ( 13)-( 15) to crack problems has been suggested in our recent work [42], though in the present study we derive its final relations in more useful separable form for the higher order cracktip fields. Note that similarly to classical elasticity, the scalar φ or one of the components of vector Φ Φ Φ can be treated as not independent except the situation when the Poisson ratio of material equals to 1/4, i.e.…”

“…In the present study, we consider the problem of derivation of an explicit solution for the higher order asymptotic in-plane crack-tip fields within the simplified SGE with single additional length scale parameter [37][38][39][40]. This solution will be obtained by using the variant of Papkovich-Neuber (PN) general solution for SGE equilibrium equations suggested in our recent works [11,41,42]. Previously, asymptotic solutions for the leading order terms within SGE with simplified and general constitutive equations have been derived in Refs.…”

Inflectional Heavy Elastica with Unilateral Contact constraint: Analytical Solution through the Curvilinear Abscissa Mapping approximation

“…Using the eq. (31,46) in (33) the general function describing the trend of the tangent angle is available:…”

“…Subsequently, a new numerical solution approach was given by [24] through a non-linear finite element model that accounts beam and contact-gap elements. Other studies dealing with the unilateral contact of Heavy Elastica are: [3] that pursue the same numerical approaches by Kooi [24], for the case of noninflectional Heavy Elastica; [33] with an analytical approach that refers to the perturbative analytical solution of Rohde [31].…”

Higher order asymptotic crack-tip fields in simplified strain gradient elasticity

“…In the present study, we consider the problem of derivation of an explicit solution for the higher order asymptotic in-plane crack-tip fields within the simplified SGE with single additional length scale parameter [37][38][39][40]. This solution will be obtained by using the variant of Papkovich-Neuber (PN) general solution for SGE equilibrium equations suggested in our recent works [11,41,42]. Previously, asymptotic solutions for the leading order terms within SGE with simplified and general constitutive equations have been derived in Refs.…”