Titlebook: Nonlocal Euler–Bernoulli Beam Theories; A Comparative Study Jingkai Chen Book 2021 The Author(s), under exclusive license to Springer Natur

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978-3-030-69787-7The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

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Nonlocal Euler–Bernoulli Beam Theories978-3-030-69788-4Series ISSN 2191-530X Series E-ISSN 2191-5318

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https://doi.org/10.1007/978-3-030-69788-4Euler-Bernoulli beam; Nonlocal theories; Peridynamics; Comparative study; Nonlocal effect; Singular solut

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Nonlocal Beam Equations,This chapter derives Euler–Bernoulli beam equations based on classical nonlocal theories, including the Eringen’s stress-gradient beam equation, the Mindlin’s strain-gradient beam equation, and the higher-order beam equation.

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Peridynamics Beam Equation,This chapter discusses the mathematical background regrading peridynamics. Then, the nonlocal beam equation built on peridynamics is proposed. It is found that the integral-form peridynamic beam equation can be reduced to the truncated-order differential equation with Taylor series expansion.

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Numerical Solutions to Peridynamic Beam,This chapter first discusses the peridynamic boundary condition treatments. Then, numerical solutions to the integral-form peridynamic beam equation is solved. Benchmark examples, including the simply-supported beam, the clamped-clamped beam and the cantilever beam, are solved with pseudo-layer boundary condition treatments.

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