Koenig H A, Burstone C J, Conant R J, Haberstock D
Am J Orthod. 1984 Nov;86(5):391-5. doi: 10.1016/s0002-9416(84)90031-9.
A new approach for the analysis of multiple-beam structures, such as headgear bows, is developed for beams which contain arbitrary curvatures, twists, and material properties. The generalized transfer matrix of a single-beam analysis is converted to a stiffness matrix and inserted into a global matrix which describes the entire system. The effect of inner bow wire size (0.044 inch and 0.051 inch) on the force system is demonstrated. The inner bow with the larger cross section shows only a slight (not clinically significant) reduction in rotational moment and buccal force applied because of its greater ability to resist deformation during the loading process. Small amounts of tooth and/or tube rotations ("play") result in a significant reduction of the crown rotational moment. With increasing rotation of the tube to the inner bow, the high lateral forces and large moments found about the long axis of the teeth are found to reduce. Symmetrical headgears are chosen to illustrate the analysis and to indicate the manner in which this approach may be used to study and design similar orthodontic appliances.
一种用于分析多梁结构（如头帽弓）的新方法被开发出来，用于包含任意曲率、扭转和材料特性的梁。单梁分析的广义传递矩阵被转换为刚度矩阵，并插入到描述整个系统的全局矩阵中。展示了内弓丝尺寸（0.044英寸和0.051英寸）对力系统的影响。横截面较大的内弓在加载过程中由于其更大的抗变形能力，仅显示出旋转力矩和颊向力的轻微（临床上不显著）降低。少量的牙齿和/或托槽旋转（“间隙”）会导致冠部旋转力矩显著降低。随着托槽相对于内弓的旋转增加，发现围绕牙齿长轴的高侧向力和大力矩会减小。选择对称头帽来说明该分析，并指出这种方法可用于研究和设计类似正畸矫治器的方式。
