材料拉压不同模量及理想塑性的圆筒变形分析

Analysis on the Deformation of Cylinder in Perfectly Plastic Material with Different Elastic Modulus in Tension and Compression

建立拉压不同模量理想塑性的厚壁圆筒变形理论,运用不同模量弹塑性理论,推导了Tresca材料圆筒的应力场及位移场的解并给出了σz为中间主应力的条件,提出了模量参数α为控制参数,并分析了不同模量参数对圆筒的变形的影响。结果表明:圆筒的弹性极限承载力,塑性区发展规律,应力场,位移场等均随着模量参数α的变化而变化,因而若采用经典的弹性理论对不同模量材料组成的构件或结构成行设计,必会带来较大的误差。

A deformation theory of cylinder in perfectly plastic materials with different modulus in tension and compression is presented. By means of the different modulus elastic - plastic theory, a general solution for calculating the Tresca materials＇ s stress and displacement field is deduced, and the condition of the Z - direction stress as the middle primary stress is given. For materials with different modulus, a controlling parameter α is introduced as a modulus parameter, and the impact on the deformation of cylinder is analyzed. The result shows that the ultimate elastic pressure, stress and displacement fields and development of plastic zone are varied with the modulus parameter. ff the classic elastic theory is adopted, it may result in rather larger errors.