材料降伏導致之結構非線性反應，於一般設計工作中多採簡化之塑性鉸之假設，但塑性鉸之假設對於斷面部分降伏、塑性區之分佈等皆無法做一準確之描述。本文旨在建立一直接而簡明之結構桿件部份斷面降伏之分析方法。
本文以荷重增量法、切線勁度矩陣，配合一綜合牛頓-拉甫森法及修正牛頓-拉甫森法計算結構節點位移向量。其次在各桿件層次求出能滿足節點變位、材料組合律、及力平衡三條件之桿端作用力。各桿件之內力與作用於節點之外力會造成不平衡力向量。本文以循環之方式修正不平衡力，直到合於所求精度。至於各桿件能滿足上述三條件之桿端力之計算，以線彈性分析之結果放大，定出一個包含所求桿端力之初始範圈。將此範圍網格化，並以三種策略逐漸收縮此範圍而得之。 Yielding is one of the reason to cause the nonlinear response of a structure. Most of the usual design works adopted a simplified plastic hinge assumption. But the simplified assumption ignored the effects such as partially yielded section, the spread of yield zone, etc.A direct and simple derivation was made in this paper for a partially yielded beam.
The incremental load method and tangent stiffness matrix were incorporated into acombined Newton-Raphson method and modified Newton-Raphson method. The joint displacement vectors were obtained sequentially in each solution step. Then the end forces of each member were obtained according to the compatibility equation and constitutive equation, etc. The unbalanced force vectors and related incremental displacement vectors were corrected continually until the convergence criterion was satisfied. The first step of calculating the end forces was to make an initial estimate of the solution range. The trial solutions were calculated at each mesh joints. Three different methods were developed to narrow down the estimated range to an accepted small tolerance.
關聯:
中華民國第四屆結構工程研討會論文集(二)=Proceedings of the 4th National Conference on Structural Engineering，頁1349-1356
