土の弾塑性変形現象は，等方硬化が塑性体積ひずみで生じるとする下負荷面モデルによって或る程度表現出来る．しかし，砂は，粘土に比して遥かに間隙比が小さく，間隙比によって著しく異なる塑性変形挙動を示すので，間隙比が大きく変化する砂の変形現象は，従来の下負荷面モデルでは適確に表現出来ない．本論文では，等方硬化の発展則に，塑性体積ひずみ速度に加えて，塑性偏差ひずみ速度を導入して，修正された砂の弾塑性構成式を提案する．また，実測データのシミュレーションにより，本構成式の妥当性を検証した．

High-frequency natural vibration analysis requires a large number of degrees of freedom. The Ritz method has the advantage that the number of degrees of freedom can be freely determined, which is advantageous for obtaining broadband and highly accurate solutions in natural vibration analysis. If the domain is discretized, Isolated Element Method must satisfy mixed boundary conditions at the boundaries of elements and elements. The number of unknowns increases when the Lagrange multiplier method is used for the Dirichlet condition. The method of identifying Lagrange multipliers using the variational principle has been proposed for the purpose of controlling the increase in the number of unknowns. In this paper, an auxiliary functional is proposed that satisfies the continuity condition for displacements between elements derived from the equivalence of potential energies on the common boundary of elements and elements, which is proved by the connected subset theorem. When a functional extended by auxiliary functions and quasi-Sobolev space are employed in a complete Hilbert space, it is shown that it converges to a unique solution by the minimum principle of the functional. As an examples of numerical analysis using this method, it are shown that a highly accurate solutions for the broadband natural frequencies of thin-walled flat plates can be obtained.