發(fā)布時間：2018-06-20 23:14

  本文選題：半隱式向后歐拉法 + Steffensen迭代法��； 參考：《巖土力學(xué)》2017年10期

【摘要】：目前,巖土工程中常用的塑性屈服準(zhǔn)則多為局部不可導(dǎo)的分段函數(shù),在隱式有限元求解中均采用顯式向前歐拉法更新應(yīng)力和Newton-Raphson迭代法求解方程。但顯式向前歐拉法容易導(dǎo)致應(yīng)力偏離屈服面和計算不收斂,而Newton-Raphson迭代法需頻繁求導(dǎo),對于分段函數(shù)而言這些方法均不利于求解。為此,提出了采用半隱式向后歐拉法和免導(dǎo)數(shù)的Steffensen迭代法聯(lián)合更新應(yīng)力與一致切線模量的方案。根據(jù)上述方案,利用ANSYS提供的User Mat模塊編寫了基于統(tǒng)一強度理論與拉破壞復(fù)合屈服準(zhǔn)則的理想塑性模型。用自定義的本構(gòu)模型模擬深埋圓形巷道彈塑性開挖過程,數(shù)值模擬結(jié)果與理論解很好地吻合,驗證了模型代碼和所提出方案的正確性和可行性。采用半隱式向后歐拉法與Steffensen迭代法相結(jié)合的手段,可簡化應(yīng)力與一致切線模量的求解,該方法避免了應(yīng)力偏離屈服面和求解流動函數(shù)偏導(dǎo),算法簡便,易于推廣應(yīng)用。
[Abstract]:At present, most of the plastic yield criteria used in geotechnical engineering are piecewise functions which are not derivable locally. The explicit forward Euler method and Newton-Raphson iterative method are used to solve the equations in implicit finite element solution. However, explicit forward Euler method can easily lead to stress deviation from yield surface and non-convergence of calculation, while Newton-Raphson iterative method requires frequent derivation, which is unfavorable for piecewise functions. For this reason, a scheme is proposed to combine the semi-implicit backward Euler method and the derivative free Steffensen iteration method to update the stress and uniform tangent modulus. According to the above scheme, an ideal plastic model based on the unified strength theory and tensile failure composite yield criterion is developed by using the user Mat module provided by ANSYS. The elastic-plastic excavation process of deep buried circular roadway is simulated by using the self-defined constitutive model. The numerical simulation results are in good agreement with the theoretical solution, which verifies the correctness and feasibility of the model code and the proposed scheme. By using semi-implicit backward Euler method and Steffensen iterative method, the solution of stress and uniform tangent modulus can be simplified. The method avoids stress deviation from yield surface and solves partial derivative of flow function. The algorithm is simple and easy to be applied.
【作者單位】： 中國科學(xué)院武漢巖土力學(xué)研究所巖土力學(xué)與工程國家重點實驗室;中國科學(xué)院大學(xué);北京科技大學(xué)土木與環(huán)境工程學(xué)院;
【基金】：國家科技支撐計劃課題(No.2012BAB08B02)~~
【分類號】：O241.82
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本文編號：2046059