Anti-plane shear waves in an elastic strip rigidly attached to an elastic half-space

We consider the anti-plane shear waves in a domain consisting of an infinite layer with a thin coating lying on an elastic half-space. The elastic properties of the coating, layer, and half-space are assumed to be different. On the free upper surface we assume the compatibility condition within the Gurtin–Murdoch surface elasticity, whereas at the plane interface we consider perfect contact. For this problem there exist two possible regimes related to waves exponentially decaying in the half-space. The first one, called transversely exponential–transversely exponential (TE–TE) regime, is related to waves described by exponential in transverse direction functions; the second, transversely harmonic–transversely exponential (TH–TE) regime, corresponds to waves in the upper layer which have the harmonic behaviour in the transverse direction. Detailed analysis of the derived dispersion equations for both regimes is provided. In particular, the effects of surface stresses, the layer thickness as well as of the ratio of shear moduli of the upper layer and half-space on the dispersion curves is analysed

ON INFLUENCE OF BOUNDARY CONDITIONS AND TRANSVERSE SHEAR ON BUCKLING OF THIN LAMINATED CYLINDRICAL SHELLS UNDER EXTERNAL PRESSURE

Buckling of a thin cylindrical sandwich shell composed of elastic isotropic layers with different elastic properties under normal external pressure is the subject of this investigation. Differential equations based on the assumptions of the generalized kinematic hypothesis for the whole sandwich are used as the governing ones. Two variants of the joint support conditions are considered at the shell edges: a) there are the infinite rigidity diaphragms inhibiting relative shears of layers along the shell edges, b) the diaphragms are absent. Using the asymptotic approach, the critical pressure and buckling modes are constructed in the form of the superposition of functions corresponding to the main stress-strain state and the edges integrals. As an example, a three-layered cylinder with the magnetorheological elastomer (MRE) embedded between elastic layers under different levels of magnetic field is studied. Physical properties of the magnetorheological (MR) layer are assumed to be functions of the magnetic field induction. Dependencies of the buckling pressure on the variant of boundary conditions and the intensity of applied magnetic field are analyzed

FINITE-ELEMENT MODELLING OF THE TYMPANIC MEMBRANE RETRACTION POCKET UNDER NEGATIVE PRESSURE IN THE TYMPANIC CAVITY

The finite-element calculation of the static stress-strain state of the middle ear was made in this paper. The malleus, incus and stapes models were constructed on the basis of tomographic data. The tympanic membrane model was obtained using the equations of elliptic hyperboloids. The tympanic membrane consists of the pars tensa and pars flaccida, which have different thicknesses and elasticity moduli. Absolute deformations of the tympanic membrane were defined at different values of negative pressure in the tympanic cavity. The critical values of elastic modulus for the pars tensa posterosuperior quadrant were found for the point at which the tympanic membrane touches the auditory ossicles. Obtained results can be used to predict the thickness of a cartilaginous graft which is overlaid on the posterosuperior quadrant of the pars tensa in order to eliminate the retraction pocket

FINITE-ELEMENT MODELLING OF THE TYMPANIC MEMBRANE RETRACTION POCKET UNDER NEGATIVE PRESSURE IN THE TYMPANIC CAVITY

The finite-element calculation of the static stress-strain state of the middle ear was made in this paper. The malleus, incus and stapes models were constructed on the basis of tomographic data. The tympanic membrane model was obtained using the equations of elliptic hyperboloids. The tympanic membrane consists of the pars tensa and pars flaccida, which have different thicknesses and elasticity moduli. Absolute deformations of the tympanic membrane were defined at different values of negative pressure in the tympanic cavity. The critical values of elastic modulus for the pars tensa posterosuperior quadrant were found for the point at which the tympanic membrane touches the auditory ossicles. Obtained results can be used to predict the thickness of a cartilaginous graft which is overlaid on the posterosuperior quadrant of the pars tensa in order to eliminate the retraction pocket

Mathematical Model for Analysis of Translational Displacements of Tooth Root

Analytical modeling of stress-strain state of a periodontal ligament in the case of the translational displacement of a tooth root was carried out. The tooth root was assumed as a rigid body. The boundary conditions corresponding to the translational displacement of the root and fixed external surface of the periodontal ligament in the dental alveolus were considered. The system of differential equations describing the periodontal ligament’s plane-strain state induced by the translational motion of the tooth were used as the governing equations. An analytical solution was found for the governing equations in the explicit form. Comparative analysis of the concentrated force generated by the prescribed translational motion of the tooth root was performed using the obtained analytical solution and the model of an incompressible periodontal ligament in the form of a circular paraboloid and hyperboloid. The mathematical model developed in this paper can be used to analyze stresses and strains in the periodontal tissue during orthodontic movement

Shell and membrane theories in mechanics and biology: from macro- to nanoscale structures

This book presents the latest results related to shells  characterize and design shells, plates, membranes and other thin-walled structures, a multidisciplinary approach from macro- to nanoscale is required which involves the classical disciplines of mechanical/civil/materials engineering (design, analysis, and properties) and physics/biology/medicine among others. The book contains contributions of a meeting of specialists (mechanical engineers, mathematicians, physicists and others) in such areas as classical and non-classical shell theories. New trends with respect to applications in mechanical, civil and aero-space engineering, as well as in new branches like medicine and biology are presented which demand improvements of the theoretical foundations of these theories and a deeper understanding of the material behavior used in such structures

Effective Young Modulus Evaluation of Bone–Titanium Biocomposite Formed Due to Complete Implant Osseointegration

The objective of study is to determine the effective Young modulus before and after the completed osseointegration process using mathematical modelling of a titanium porous structure. A novel model is proposed in the form of 3D arrays of Gibson-Ashby cells with rigid clamping of horizontal beams resting on elastic foundation. Calculations made on the basis of the developed model are compared with known models and literature data. The assumption is proved that the osseointegration process due to the bone tissues ingrowth into the pores of titanium implant could affect the Young modulus increasing its value in proportion to porosity of a specimen