Krylov Subspace Accelerated Newton Algorithm: Application to Dynamic Progressive Collapse Simulation of Frames
Krylov Subspace Accelerated Newton Algorithm: Application to Dynamic Progressive Collapse Simulation of Frames
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DOI：
10.1061/(asce)st.1943-541x.0000143
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发表时间：
2010-05
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影响因子：
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通讯作者：
M. Scott;G. Fenves
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文献类型：
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作者：
M. Scott;G. Fenves
基于Krylov子空间的加速牛顿算法被应用于求解结构平衡的非线性方程。该算法使用低秩最小二乘分析来推进结构状态发生最大变化的自由度自由度处的平衡搜索；然后，它使用修改后的牛顿计算来校正剩余自由度的较小变化。该算法适合模拟框架的动态渐进倒塌分析，其中屈服和局部倒塌机制在少量自由度处形成，而其余结构部件的状态相对线性。此外，该算法能够解决由切线刚度矩阵中的近似误差引起的错误搜索方向。数值算例表明，在钢筋混凝土和钢框架的动态渐进倒塌模拟中，Krylov子空间算法比Newton-Raphson算法具有更大的收敛半径和更少的矩阵分解次数。 DOI：10.1061/ASCEST.1943-541X.0000143 CE 数据库主题词：算法；失败；非线性分析；进行性塌陷；钢框架。作者关键词：算法；坍塌;非线性分析；渐进式失败。
An accelerated Newton algorithm based on Krylov subspaces is applied to solving nonlinear equations of structural equilib- rium. The algorithm uses a low-rank least-squares analysis to advance the search for equilibrium at the degrees of freedom DOFs where the largest changes in structural state occur; then it corrects for smaller changes at the remaining DOFs using a modified Newton computation. The algorithm is suited to simulating the dynamic progressive collapse analysis of frames where yielding and local collapse mechanisms form at a small number of DOFs while the state of the remaining structural components is relatively linear. In addition, the algorithm is able to resolve erroneous search directions that arise from approximation errors in the tangent stiffness matrix. Numerical examples indicate that the Krylov subspace algorithm has a larger radius of convergence and requires fewer matrix factorizations than Newton-Raphson in the dynamic progressive collapse simulation of reinforced concrete and steel frames. DOI: 10.1061/ASCEST.1943-541X.0000143 CE Database subject headings: Algorithms; Failures; Nonlinear analysis; Progressive collapse; Steel frames. Author keywords: Algorithms; Collapse; Nonlinear analysis; Progressive failure.