厚板哈密顿求解体系及其变分原理与正交关系

HAMILTONIAN SOLUTION SYSTEM FOR THICK PLATES AND ITS VARIATIONAL PRINCIPLE AND ORTHOGONALITY RELATIONSHIP

  • 摘要: 将哈密顿求解体系推广应用于Reissner-Mindlin厚板问题.首先导出了厚板哈密顿对偶微分方程,然后采用换元乘子法导出了厚板哈密顿变分原理的泛函表示式,最后提出并证明了厚板理论的两个正交关系.厚板哈密顿体系的理论成果将为研究厚板解析解和有限元解提供新的有效工具.

     

    Abstract: The Hamiltonian solution system is generalized to the Reissner-Mindlin thick plate problems. The Hamiltonian dual differential equations for thick plates are derived and the functional expressions of Hamiltonian variational principle are obtained using the variable substitution and multiplier method. Two orthogonality relationships of the thick plate theory are proposed and demonstrated. The Hamiltonian solution system for thick plates provides a new effective tool for the development of analytical solutions and finite element solutions of thick plates.

     

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