Purpose

The purpose of the present study is to explore the incomplete substitution of the simplex triangular finite element by either of two models: one evolving out as part of the element flexibility, and the other as part of the element stiffness.

Design/methodology/approach

The elastic energy stored in each of the units under stress or strain decides on stiffer and weaker responses. The pertaining Rayleigh quotient in terms of the flexibility matrices allows bounding the distance of the spring cell models to the finite element in dependence of the triangle configuration.

Findings

Despite a superiority of the flexibility cell concept observed in computations, the study reveals constellations of shape and stressing of the triangle that favour the stiffness concept. The latter is seen to behave stiffer than its flexibility counterpart and produces results more distant to the finite element in most cases.

Research limitations/implications

The difference between the stiffness and the flexibility approach to spring cells is investigated for triangular elements in dependence of the geometrical configuration under specific conditions of stressing. This suffices to refute an exclusive superiority of the flexibility concept although largely true.

Practical implications

The results of the investigation appear useful in deciding between the spring cell models depending on the case of a spring lattice application.

Originality/value

The flexibility approach to the spring cell is not widely known yet. This cell model deserves a study on performance and comparison to the different, more common stiffness cell model.

中文翻译：

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基于刚度与柔韧性的三角弹簧盒–性能分析

目的

本研究的目的是通过两种模型中的一种来探索单纯形三角形有限元的不完全替代：一种演化为单元柔韧性的一部分，另一种演化为单元刚度的一部分。

设计/方法/方法

在应力或应变下存储在每个单元中的弹性能决定了刚度和弱度的响应。就柔韧性矩阵而言，相关的瑞利商允许根据三角形构造将弹簧单元模型的距离限制到有限元。

发现

尽管在计算中观察到了柔性单元格概念的优越性，但这项研究揭示了有利于刚度概念的三角形形状和应力星座。在大多数情况下，后者的行为比其柔韧性要强，并且产生的结果与有限元的距离更远。

研究局限/意义

对于三角形单元，根据在特定应力条件下的几何构型，研究了弹簧单元的刚度和柔韧性方法之间的差异。尽管基本上是正确的，但这足以驳斥灵活性概念的排他性优势。

实际影响

研究的结果似乎对于根据弹簧点阵应用的情况来确定弹簧单元模型之间很有用。

创意/价值

弹簧单元的柔性方法尚未广为人知。该单元模型值得研究性能，并与其他更常见的刚度单元模型进行比较。