A simultaneous adaptive mesh refining and coarsening algorithm in high-order element-based upper bound finite element method in non-homogeneous soils
In geotechnical engineering,upper bound finite element method with adaptive mesh refinement often evaluates the plastic failure area in a posterior manner,which may cause an excessive refinement in the buffer zone between rigid and plastic zones and lead to a high computational cost.Meanwhile,the initial mesh for the adaptive upper bound finite element method should not be too sparse to avoid the large error caused by the over-rigidity of model,as it can induce subsequent adaptive refinement to deviate from the correct direction.In this study,with a combination of six-node triangular elements and a second-order cone programming model,an upper bound finite element method with simultaneous adaptive mesh refining and coarsening algorithm is proposed.This method can automatically determine both active elements and inactive elements using plastic power dissipation-based estimators.For each adaptive step,those active elements are automatically refined and those inactive ones are thus coarsened,which can achieve the purpose of reducing the total number of elements and improving computational accuracy.The proposed method is then extended to the stability analysis in non-homogeneous soils,and numerical implementation of the proposed method is discussed.Two examples including tunnel face stability and failure of active trapdoors in non-homogeneous soils are analyzed to evaluate the validity of the proposed method through a series of parameter analysis.
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