Shell and Membrane Theories in Mechanics and Biology
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Shell and Membrane Theories in Mechanics and Biology

From Macro- to Nanoscale Structures
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Holm Altenbach
45, Advanced Structured Materials
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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.

On the theories of plates and shells at the nanoscale.- Homogenization approach in the theory of plates and shells.- Wavelet analysis of nonlinear mechanics of shells.- Solid mechanics modeling in ophthalmology.- Theory of shells and theory of curvilinear rods: A comparative analysis.- Initial-value problems in general asymptotic theory for thin walled elastic structures.- Second-order isotropic and anisotropic plate theories.- Actual problems of nanomechanics.- Analysis of free vibrations of multi-walled carbon nanotubes based on theories of orthotropic cylindrical shells and non-local elasticity.- A shell theory for CNTs of arbitrary chirality.- The application of shell model to biological membranes.- Studying free vibrations of totally reconstructed middle ear based on the plate theory and FEM simulation.- Concerning approaches to modeling and restoration of inhomogeneous initial stress fields in plates.- Some problems of equilibrium and stability of nonlinearly elastic circular membranes.- New approach for studying nonlinear dynamic response of thin plates in a viscoelastic medium.- Aspiration of a nonlinear elastic spherical membrane.- Movement modelling of soft microrobot of amoebalike type in the heterogeneous environment.- Identification of the elastic modulus of polymeric materials based on compression of thin-walled cylindrical specimens.- On gradient theories of plates and shells with applications to nanomechanics.- Nanoplate stability.- Asymptotic solutions for thin layers in articular contact.- Three-dimensional exact analysis of functionally graded and laminated piezoelectric plates.
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.

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