Nonlocal Finite Element Analysis of Strain‐Softening Solids
Nonlocal Finite Element Analysis of Strain‐Softening Solids
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DOI：
10.1061/(asce)0733-9399(1987)113:1(89
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发表时间：
1987
期刊：
影响因子：
--
通讯作者：
Z. Bažant;Ta-Peng Chang
中科院分区：
文献类型：
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作者：
Z. Bažant;Ta-Peng Chang
给出了叠瓦状非局部应变软化连续体的二维有限元列式，并进行了数值验证。与通常的局部有限元程序的唯一区别是，某些有限元是重叠的，即它们规则地重叠，而跳过中间网格节点。单元叠置的特征是生成适当的整数矩阵，该矩阵给出每个有限单元的节点数和与每个局部单元重叠的叠置单元的个数。未知位移的数量保持与本地有限元代码相同，而有限元的数量大约增加一倍。数值结果表明，随着网格的细化，可以得到稳定的多单元宽度的二维应变软化区，并且具有较好的收敛特性。对于载荷-位移图、应变软化带上的应变分布以及开裂所耗费的总能量，都证明了收敛。结果还表明，局部公式表现出不正确的收敛；它们收敛到因失效而导致的能量耗散为零的解，这在物理上是不可接受的。通过使加载步长很小，使得两个互不重叠的单元在同一加载步长内不能进入应变软化区，从而避免了应变软化引起的稳定性问题。
A two-dimensional finite element formulation for imbricate nonlocal strain-softening continum is presented and numerically demonstrated. The only difference from the usual, local finite element codes is that certain finite elements are imbricated, i.e., they regularly overlap while skipping the intermediate mesh nodes. The element imbrication is characterized by generating proper integer matrices that give the numbers of the nodes for each finite element and the numbers of the imbricate elements overlapping each local element. The number of unknown displacements remains the same as for a local finite element code, while the number of finite elements approximately doubles. Numerical results show that stable two-dimensional strain-softening zones of multiple-element width can be obtained, and that the solution exhibits proper convergence as the mesh is refined. The convergence is demonstrated for the load-displacement diagrams, for the strain profiles across the strain-softening band, and for the total energy dissipated by cracking. It is also shown that the local formulations exhibit incorrect convergence; they converge to solutions for which the energy dissipation due to failure is zero, which is physically unacceptable. Stability problems due to strain-softening are avoided by making the loading steps so small that no two mutually nonoverlapping elements may enter the strain-softening regime within the same load step.