Problems of Concentrated Loads in Microstructured Solids Characterized by Dipolar Gradient Elasticity

摘要: This work studies the response of bodies governed by dipolar gradient elasticity to concentrated loads. The use theory is intended here model material microstructure and incorporate size effects into stress analysis in a manner that classical cannot afford. A simple but yet rigorous version generalized theories Toupin [1] Mindlin [2] employed involves an isotropic linear only one constant (the so-called coefficient) additional standard Lame constants. theory, which can be viewed as first-step extension assumes strain-energy density function, besides its dependence upon strain terms, depends also on gradients [3]. Twodimensional configurations form either half-space (Flamant-Boussinesq type problem) or full-space (Kelvin are treated loads taken line forces. problems enjoy important applications various areas, e.g., Contact Mechanics Tribology. Also, Flamant-Boussinesq Kelvin solutions serve pertinent Green’s functions multitude analyzed Boundary Element Method. Our main concern determine possible deviations from predictions elastostatics when more refined attack problems. Of special importance behavior new near point application where pathological singularities exist solutions. solution method based integral transforms exact. present results show departure ones Indeed, bounded displacements predicted even at points Such displacement fields seems natural than singular