YAO Zheng, ZHENG Chang-liang. Inter-Belt Analysis of the Integral-Form Nonlocal Constitutive Relation[J]. Applied Mathematics and Mechanics, 2015, 36(4): 362-370. doi: 10.3879/j.issn.1000-0887.2015.04.003
Citation: YAO Zheng, ZHENG Chang-liang. Inter-Belt Analysis of the Integral-Form Nonlocal Constitutive Relation[J]. Applied Mathematics and Mechanics, 2015, 36(4): 362-370. doi: 10.3879/j.issn.1000-0887.2015.04.003

Inter-Belt Analysis of the Integral-Form Nonlocal Constitutive Relation

doi: 10.3879/j.issn.1000-0887.2015.04.003
Funds:  The National Natural Science Foundation of China(11202040)
  • Received Date: 2014-09-26
  • Rev Recd Date: 2014-12-17
  • Publish Date: 2015-04-15
  • Based on the Hamilton theory, the constitutive relation was investigated for the nonlocal linear elasticity originally proposed by Eringen. Eringen’s nonlocal equations can be written in the integral form and the differential form. The differential form with the relatively simple mathematical formulation, had been widely used in recent years. For the integral form of the nonlocal elastic theory, solving the integro-differential equations was challenging for numerical process. In the analytical structural mechanics, the integro-differential equations in time-delay problems had been solved with the inter-belt theory. According to the simulative relations between the analytical dynamics and the analytical structural mechanics, the inter-belt theory was introduced into the integral-form constitutive equations of the nonlocal theory, and hence the integro-differential equations were numerically solved with high precision. Then the fundamental theory and computational algorithm were applied to dynamic problems of nonlocal rod vibration. The numerical experiments demonstrate validity of the present method and potential of the symplectic system algorithm in solving nonlocal mechanics problems.
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