同心曲线分布荷载下圆形各向同性板的精细计算

IF 0.7 4区 材料科学 Q4 MATERIALS SCIENCE, CHARACTERIZATION & TESTING Strength of Materials Pub Date : 2024-02-29 DOI:10.1007/s11223-024-00605-z
V. I. Shvabyuk, S. V. Rotko, V. V. Shvabyuk, O. S. Prykhodko
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引用次数: 0

摘要

利用复变解析函数的线性共轭方法解决了边缘铰接的圆形横向各向同性板弯曲问题,外表面受到沿同心曲线分布的力的加载。用于记录问题的应力和变形特征的复数势能在集中力加载点处具有特定特征,研究了它们的性质,并将其应用于现有的条件集中加载。为了求解,使用了包含横向剪切应变和横截面缩减的改进横向板弯曲模型方程,与其他改进理论不同的是,这些改进的公式是先进的。复势中的常数是根据边界条件和矩的共轭条件以及横截面沿加载线旋转的广义角度确定的。采用 Timoshenko 和 Woinowsky-Krieger 的方法,从圆形加载解作为一个特殊案例,得到了中心集中力加载板的解。对于这两种情况,都计算了板中心和边缘的细化法向径向应力和周向应力。数据汇总在表格和图表中。模型和数值结果表明,板横向各向异性的增加会从根本上改变其横截面的应力分布模式,直至改变外表面的径向应力符号。经典的板弯曲模型以及 Timoshenko 和 Reissner 等人的改进模型都不适用于这种情况。
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Refined Calculation of a Circular Transtropic Plate Under Concentric Curve-Distributed Loading

The method of linear conjugation of analytical functions of complex variable was used to solve the problem of circular transversally isotropic plate bending hinged on the edge and loaded over the outer surface by the force distributed along the concentric curve. The complex potentials employed for registering the stress and deformation characteristics of the problem can possess the specific features at the concentrated force loading points, their nature was investigated and applied to the existing loading as conditionally concentrated. For getting the solution, the equation for the refined transtropic plate bending model was used that includes transverse shear strains and cross-sectional reductions, and, unlike other refined theories, the formulas with those refinements are advanced. The constants in the complex potentials were established with the boundary conditions and conjugation conditions for the moments and generalized angles of cross-section rotation along the loading line. With the approach by Timoshenko and Woinowsky-Krieger, from the circular loading solution, as a particular case, the solution for the centered concentrated force-loaded plate was obtained. For both cases, the refined normal radial and circumferential stresses were calculated in the center and on the edge of the plate. The data are summarized in tables and graphs. The model and numerical results show that an increase in the transverse plate anisotropy can radically change stress distribution patterns in its transverse cross-sections, up to the change in the radial stress signs on the outer surfaces. The classical model of plate bending and refined models such as by Timoshenko and Reissner are inapplicable in this case.

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来源期刊
Strength of Materials
Strength of Materials MATERIALS SCIENCE, CHARACTERIZATION & TESTING-
CiteScore
1.20
自引率
14.30%
发文量
89
审稿时长
6-12 weeks
期刊介绍: Strength of Materials focuses on the strength of materials and structural components subjected to different types of force and thermal loadings, the limiting strength criteria of structures, and the theory of strength of structures. Consideration is given to actual operating conditions, problems of crack resistance and theories of failure, the theory of oscillations of real mechanical systems, and calculations of the stress-strain state of structural components.
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