基于平衡的有限元分析雷斯纳-明德林板曲问题
Zdzisław Więckowski1, Paulina Świątkiewicz2
1Independent Researcher, 90-001 Łódź, Poland.
Materials (Basel, Switzerland)
|November 13, 2025
概括
本研究介绍了一种基于应力的有限元素方法,用于Reissner-Mindlin板曲问题. 它应用特定元素来近似应力场,并分析硬边界条件以获得准确的数值解决方案.
科学领域:
- 固体力学 固体力学是什么
- 计算工程 计算工程
- 有限元分析 有限元分析
背景情况:
- 赖斯纳-明德林板块理论解释了横切削变形,对于厚板块至关重要.
- 准确的应力场近似值对于分析负载下的板块行为至关重要.
- 有限元素方法为解决复杂的机械问题提供了强大的工具.
研究的目的:
- 为Reissner-Mindlin板曲问题提出一种新的基于应力的有限元素方法.
- 用特定的有限元来评估应力近似的准确性.
- 分析硬边界条件对板曲解决方案的影响.
主要方法:
- 应用矩形Bogner-Fox-Schmit和三角形Hsieh-Clough-Tocher元素的方法.
- 对于静态允许的应力场的Southwell应力函数的近似值.
- 使用基于位移的元素 (12和22自由度) 来进行参考和误差估计.
- 对2D或硬边界条件变体的分析.
主要成果:
- 拟议的基于应力的有限元素方法提供了一种方法来近似板块中的应力场.
- 使用指定的元素获得的数值结果提供了对板曲行为的洞察.
- 与基于位移的元素进行比较,有助于对基于应力解决方案的误差估计.
- 该研究分析了硬边界条件的具体影响.
结论:
- 基于应力的有限元素方法是对莱斯纳-明德林板曲问题的可行方法.
- 博格纳 - 福克斯 - 施密特和希希 - 克劳 - 托切尔元素对于近似应力函数是有效的.
- 了解硬边界条件的影响对于准确的板块分析至关重要.
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