以彈塑性模式描述多維加載下的塑性行為

Abstract

材料或構件持續受到外力加載其力學行為會由彈性進入塑性，若是只考慮一維狀態下(單拉、單壓、單扭)其彈性與塑性行為可以很簡單地描述，然而若是考慮多維加載狀態下，描述材料塑性行為就會變得比較複雜，這點也可以在側推分析方法(pushover analysis)中發現。目前台灣耐震設計時所使用的側推分析方法往往只能個別考慮單一個方向(幾乎單調遞增)地震力造成的影響，然而在現實狀況中地震力方向並不單單只有一個方向，因此研究雙向地震對建築物造成的影響是具有其探討價值。而本研究提出的彈塑性模型可以模擬材料或構件多方向的加載，以及模擬建築物受雙方向的地震力時屋頂剛心位移以及基底剪力的關係，並求得其閉合正解。 在塑性行為中降伏面演化研究也是重要的一環，目前大多數的研究都是利用既有模型推導出能夠模擬單顆降伏面之複雜的數學式，而這些理論雖然能夠準確地描述單顆降伏面，但無法描述降伏面全程演化之行為。 而本研究之目的在於利用物裡意義明確之彈塑性元件來描述材料、構件甚至是建築進入塑性後的行為，像是包辛格效應(Bauschinger effect)、走動硬化(kinematic hardening)、等向軟硬化(isotropic hardening-softening)、混合走動等向軟硬化(mixed-kinematic-isotropic hardening)等行為，並求得其閉合正解。

When a material or component is continuously loaded by external force, its mechanical behavior changes from elasticity to plasticity. If only a one-dimensional loading state (uniaxial tension or compression) is considered, its elastoplastic behavior can be described very simply. However, if multi-dimensional loading is considered, it becomes more complicated to describe the elastoplastic behavior of the material. It can also be found in pushover analysis. The seismic design only considers the impact caused by the seismic force in a single direction. However, in reality, the direction of the earthquake is not just one direction. Therefore, studying the impact of a two-way earthquake on buildings is of great value. Elastoplastic models proposed in this study can be used to simulate the multi-directional loading of materials or components, and even to simulate the relationship between the displacement of the center of rigidity of the roof and the shear force of the base when the building is subjected to earthquake forces in two directions. The research on the evolution of the yield surface in the plastic behavior is an important part. However, most of the research uses existing models to derive complex mathematical formulas that can simulate the single yield surface. Although these theories can accurately describe the single yield surface, there is no way to describe the evolutionary behavior of the yielding surface. This study aims to model the elastoplastic behavior of materials, components and buildings by using elastoplastic models capable of describing the Bauschinger effect, kinematic hardening-softening, isotropic hardening-softening, mixed-kinematic-isotropic hardening-softening, and derive the closed-form solution of the response to input rectilinear force path.