考虑剪切影响的杆内时本构方程

Member endochronic constitutive equations including shearing distortions

建立考虑剪切影响时等截面直杆内时的本构方程.将杆端位移、杆变形、截面内力分为不考虑剪切变形和只考虑剪切变形两部分,采用有限元方法并利用虚位移原理和截面内时本构关系,得到杆单元本构关系的初步形式.通过引入杆平衡条件以及两部分挠度之和等于全挠度的几何条件,将杆单元本构关系原始形式中剪力行和弯矩行的两部分加以合并,导出了按增量初内力法表达的杆内时本构方程.结果表明,剪切变形将影响杆单元初始刚度矩阵、杆端等效剪力和等效弯矩、杆端塑性剪力增量和塑性弯矩增量;当剪切系数为零时,本模型退化为既有研究中不考虑剪切变形的杆内时模型.本模型适用于按增量初内力法进行的考虑杆剪切变形的结构弹塑性分析.

Member endochronic constitutive equations including shearing distortions are established for straight members having uniform properties along their lengths. Firstly, nodal displacements, member deformations and section internal forces are divided into two parts. One part didn't include the shearing effect and another part only took into account shearing distortions. Then guided by the finiteelement concept and using the principle of virtual displacements and the section endochronic constitutive equation, the original form of member constitutive equations was deduced. Finally, through introducing equilibrium relationships and total deflections of the member, the nonshearing part and the shearing part in the original form were combined together and the member endochronic model were obtained in the form of the incremental initialforce method.The results show that shearing distortions have the effects on the initial stiffness matrix, equivalent shearing loads and bending moment loads, as well as the increments of plastic shears and bending moments on the nodes. For the case of shearing coefficients being zero, the new model changes into the member endochronic model neglecting the shearing effect in previous researches. The model in this paper can be used in the structural elastoplastic analysis based on the incremental initialforce method, where shearing distortions of the members are taken into account.