Shell and Membrane Theories in Mechanics and Biology: From Macro- to Nanoscale Structures (Advanced Structured Materials Book 45)

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. Front Matter....Pages i-xi On Some Classes of 3D Boundary-Value Problems of Statics and Dynamics of Plates and Shells....Pages 1-23 On the Theories of Plates and Shells at the Nanoscale....Pages 25-57 Chaotic Vibrations of Conical and Spherical Shells and Their Control....Pages 59-80 Nonclassical Shell Theories in Ocular Biomechanics....Pages 81-97 Linear Oscillations of Suspended Graphene....Pages 99-107 On Discrete-Kirchhoff Plate Finite Elements: Implementation and Discretization Error....Pages 109-131 Shell Theory-Based Estimation of Local Elastic Characteristics of Biological Cells....Pages 133-146 On the Direct Approach in the Theory of Second Gradient Plates....Pages 147-154 A Shell Theory for Carbon Nanotube of Arbitrary Chirality....Pages 155-167 Finite Axisymmetric Deformation of an Inflatable Anisotropic Toroidal Membrane....Pages 169-186 Simulation of Cardiac Cell-Seeded Membranes Using the Edge-Based Smoothed FEM....Pages 187-212 Determining the Modulus of Elasticity for Polymer Materials by Numerical Testing Thin-Walled Double-Layer Circular Shells....Pages 213-222 Three-Dimensional Exact Analysis of Functionally Graded Laminated Composite Plates....Pages 223-241 Prediction of Eigenfrequencies of the Middle Ear Oscillating System After Tympanoplasty and Stapedotomy....Pages 243-265 A New Approach for Studying Nonlinear Dynamic Response of a Thin Fractionally Damped Plate with 2:1 and 2:1:1 Internal Resonances....Pages 267-288 On Stability of Inhomogeneous Elastic Cylinder of Micropolar Material....Pages 289-300 A New Approach for Studying Nonlinear Dynamic Response of a Thin Fractionally Damped Cylindrical Shell with Internal Resonances of the Order of $$\varepsilon $$ ....Pages 301-321 Featuring the latest results on the topic, this monograph explains how to use a multidisciplinary approach from macro- to nanoscale in characterizing and designing shells, plates, membranes and other thin-walled structures in mechanics and biology.