Nonlocal Euler Bernoulli Beam Theories
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Nonlocal Euler–Bernoulli Beam Theories
This book presents a comparative study on the static responses of the Euler-Bernoulli beam governed by nonlocal theories, including the Eringen’s stress-gradient beam theory, the Mindlin’s strain-gradient beam theory, the higher-order beam theory and the peridynamic beam theory. Benchmark examples are solved analytically and numerically using these nonlocal beam equations, including the simply-supported beam, the clamped-clamped beam and the cantilever beam. Results show that beam deformations governed by different nonlocal theories at different boundary conditions show complex behaviors. Specifically, the Eringen’s stress-gradient beam equation and the peridynamic beam equation yield a much softer beam deformation for simply-supported beam and clamped-clamped beam, while the beam governed by the Mindlin’s strain-gradient beam equation is much stiffer. The cantilever beam exhibits a completely different behavior. The higher-order beam equation can be stiffer or softer depending on the values of the two nonlocal parameters. Moreover, the deformation fluctuation of the truncated order peridynamic beam equation is observed and explained from the singularity aspect of the solution expression. This research casts light on the fundamental explanation of nonlocal beam theories in nano-electromechanical systems.
Non-local Structural Mechanics
Serving as a review on non-local mechanics, this book provides an introduction to non-local elasticity theory for static, dynamic and stability analysis in a wide range of nanostructures. The authors draw on their own research experience to present fundamental and complex theories that are relevant across a wide range of nanomechanical systems, from the fundamentals of non-local mechanics to the latest research applications.
Systems Theory for Engineering Practice
This book presents cognition of the universality of systems theory thinking by using some ordinary physical phenomena and their methods in study, of which the involved treatments are consistent with the viewpoint of systems theory. It contains the collective actions of classical vibration of many bodies and wave, the extreme value problem in natural world, status of electrons in atom-molecule and metals, Ising model in phase transition and elementary excitation in solid, multi-objective optimization in a system, description of effective media approximation, certainty in uncertain phenomena, all these reflect the cooperative/synergetic effects, wholeness of group actions, “unity of opposites” inside a system, and collective phenomena in a system completely. The relevant methodologies for systems theory are organic combination and synergism of both “reductionism” and “holism” instead of “confrontation” or “separation” of them, which could be used in dealing with analogous problems in systems science and engineering fields in response to the idiom of “stones from other hills being good for polishing this jade” and “comprehend by analogy”, so as to promote the transformation of wisdom to productivity. The authors wish this work could play its role as a paving stone to serve the research and application of systems theory. This book can be used as a textbook for postgraduate and advanced undergraduate students in relevant majors, and a reference book for scientists and practitioners in related fields.