Shell and Membrane Theories in Mechanics and Biology

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.

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.

1 On Some Classes of 3D Boundary-Value Problems of Statics and Dynamics of Plates and Shells,- 2 On the Theories of Plates and Shells at the Nanoscale.- 3 Chaotic Vibrations of Conical and Spherical Shells and Their Control.- 4 Nonclassical Shell Theories in Ocular Biomechanics.- 5 Linear Oscillations of Suspended Graphene.- 6 On Discrete-Kirchhoff Plate Finite Elements: Implementation and Discretization Error.- 7 Shell Theory-Based Estimation of Local Elastic Characteristics of Biological Cells.- 8 On the Direct Approach in the Theory of Second Gradient Plates.- 9 A Shell Theory for Carbon Nanotube of Arbitrary Chirality.- 10 Finite Axisymmetric Deformation of an Inflatable Anisotropic Toroidal Membrane.- 11 Simulation of Cardiac Cell-Seeded Membranes Using the Edge-Based Smoothed FEM.- 12 Determining the Modulus of Elasticity for Polymer Materials by Numerical Testing Thin-walled Double-layer Circular Shells.- 13 Three-Dimensional Exact Analysis of Functionally Graded Laminated Composite Plates.- 14 Prediction of Eigenfrequencies of the Middle Ear Oscillating System after Tympanoplasty and Stapedotomy.- 15 A New Approach for Studying Nonlinear Dynamic Response of a Thin Fractionally Damped Plate with 2:1 and 2:1:1 Internal Resonances.- 16 On Stability of Inhomogeneous Elastic Cylinder of Micropolar Material.- 17 A New Approach for Studying Nonlinear Dynamic Response of a Thin Fractionally Damped Cylindrical Shell with Internal Resonances of the Order of e.