Plastisches Knicken der Wandung von Hohlzylindern und einige andere Faltungserscheinungen an Schalen und Blechen

On Some Approximate Methods for the Tensile Instabilities of Thin Annular Plates

“…For all practical purposes, it is the lowest positive eigenvalue, Λ 1 , which is of interest, and we shall focus our attention on this quantity; for simplicity of notation we shall refer to it as Λ. Since according to (8) the expression of Λ depends explicitly on a/b, it is useful to also use Λ * := σ * b 2 h/D as an alternative choice for the eigenvalues of (13) and (14); this will be subject to the same restrictions as stated above.…”

“…When this applied load reaches a critical value, the plate undergoes elastic buckling circumferentially, a phenomenon referred to as elastic wrinkling in the literature. Geckler [8] provided a first approximate study of this problem by considering the plastic regime, and his work was then followed by many others (cf. [3, pp.…”

A study on the buckling behaviour of aluminium alloy sheet in deep drawing with macro-textured blankholder

“…Geckeler [15] proposed a mathematical analysis for wrinkling behaviour in the deep drawing process without blankholder, using which, the critical stress and wrinkling wave number can be determined. Senior [16] extended Geckeler's results using an energy method, in his research, the circular flange was assumed as a one-dimensional beam, buckling occurred when the compressive stress in the circumferential direction reached a critical value.…”

Research Development on Wrinkling Prediction and Suppression for Sheet Hydroforming of Thin-walled Deep Drawing Parts

“…。 以拉深零件中典型的球底件和平底件为例，按 照板料变形程度可以将零件分为传力区和变形 区 [8] ，而若以零件几何区域为标准可以分为法兰区 和悬空区(平底件为直壁区)。所以起皱缺陷也因此 可以分为外皱(法兰区起皱)和内皱(悬空区起皱) [9] 。 从拉深过程中板材的力学状态分析，外皱和内 皱均是板料在环向压应力的作用下由平面内变形变 为平面外的屈曲变形导致的分叉失稳，从而偏离基 本平衡路径进入次级平衡路径 [10] 。因而如何准确地 预测分叉点成了预测和控制起皱的关键因素。对于 外皱和内皱的研究，一个世纪来研究的思路大体相 同。通过理论研究，包括近似能量法和分叉理论(解 析能量法)，得到起皱的临界压应力 [11] ，并逐渐从单 轴的一维求解发展至平面坐标系的二维求解 [12] 。而 后随着有限元分析技术的发展，以理论分析为基础 并借助数值模拟，最终进行试验验证成了一种行之 有效的研究方法 [13] …”

“…于 1961 年系统地分析 了弹性稳定性理论，并以能量理论为基础推导了方 板受压时发生屈曲的临界状态公式。但是包括 GECKELER [11] 和 SENIOR [19] 以及 KAFTANOGLU [21] 在内的学者都是在一维的基础上推导出临界应力， 而这种预测只有在法兰区的宽度远小于板材的半径 时，预测结果才较为准确，所以 YU 等 [12] 通过建立 柱坐标系进行了二维的起皱预测，得到了板材发生 弹性屈曲和塑性屈曲的临界条件，并对塑性变形时 能够抑制起皱的最小压边力进行了计算。其柱坐标 系中临界起皱能∆U 以及塑性变形能∆T 的表达式在 后来的研究中得到了广泛应用，成为了通过能量法 则进行起皱预测的一个通用公式，其形式具体如下 ( ) …”