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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Stabilized mixed finite element formulations for materially nonlinear partially saturated two-phase media
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Stabilized mixed finite element formulations for materially nonlinear partially saturated two-phase media

机译：用于材料非线性部分饱和的两相介质的稳定的混合有限元公式

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摘要

Standard and enhanced (BBAR or EAS) low order finite elements applied to the problem of consolidation of two-phase nonlinear continua do not satisfy the LBB condition when the same interpolation functions are used for both displacement and pore pressure fields. Strong spatial pressure oscillations are the main consequence of the LBB condition violation. The class of direct stabilized methods, widely used in the field of fluid mechanics, is a powerful tool to circumvent violation of the aforementioned condition. Three stabilized formulations, designed for the problem of consolidation of fully or partially saturated media are presented: Galerkin/least-squares (GLS) with the least-squares term construction based on the residuum of the local fluid mass conservation equation; the pressure stabilized formulation (FPL) in which the rate of the pore pressure Laplacian (residual free in the incompressibility limit) is added to the fluid mass conservation equation; and, finally, a stabilized formulation in which the stabilization term is constructed based on the rate of the residuum of the local momentum equation. An h-convergence study and test problems for the three stabilized schemes are discussed.
机译：当对位移和孔隙压力场使用相同的插值函数时，应用于两相非线性连续体固结问题的标准和增强型（BBAR或EAS）低阶有限元不满足LBB条件。强烈的空间压力振荡是违反LBB条件的主要后果。在流体力学领域中广泛使用的一类直接稳定方法是一种有效的工具，可以避免违反上述条件。提出了三种针对完全饱和或部分饱和介质固结问题的稳定公式：Galerkin /最小二乘（GLS），具有基于局部流体质量守恒方程的残差的最小二乘项构造；压力稳定剂（FPL），其中将孔隙压力拉普拉斯算子的速率（在不可压缩极限内残留）添加到流体质量守恒方程中；最后，根据局部动量方程的残差率构造稳定项。讨论了三种稳定方案的h收敛研究和测试问题。

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