Kinetic- and Strain-Energy Approaches in the Thermal Analysis of Constrained Mechanical Systems: A Comparative Study

IF 1.9 4区 工程技术 Q3 ENGINEERING, MECHANICAL
Moataz Abdalla, Ahmed A. Shabana
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Abstract

Abstract Despite the unconstrained thermal expansion is assumed stress-free, the conventional FE approach requires formulating elastic forces, and this in turn leads to elastic stresses. A displacement-based formulation, on the other hand, can be used to address this limitation by converting the thermal energy to kinetic energy instead of strain energy. The fundamental differences between the strain- and kinetic-energy approaches are discussed. It is shown that the unconstrained thermal expansion predicted using the kinetic-energy approach is independent of the continuum constitutive model, and consequently, such a formulation can be used for both solids and fluids. The displacement (kinetic) and strain (stress) formulations are discussed to shed light on the mechanism of thermal expansion at the macroscopic level. The thermal-expansion displacement formulation (TEDF) and position-gradient multiplicative decomposition into thermal and mechanical parts are used to compute the thermal stresses due to boundary and motion constraints (BMC). TEDF implementation issues are discussed and constant matrices evaluated at a preprocessing stage after applying sweeping matrix technique to eliminate rigid-body thermal-displacement translational modes are identified. Furthermore, the softening effect due to the constitutive-model dependence on the temperature is investigated at high temperatures. Numerical results are presented to show fundamental differences between the TEDF approach that converts heat energy to kinetic energy and conventional FE approach that converts heat energy to strain energy that produces elastic stresses.
约束机械系统热分析中的动能和应变能方法:比较研究
尽管假设无约束热膨胀是无应力的,但传统的有限元方法需要制定弹性力,而这反过来又导致弹性应力。另一方面,基于位移的公式可以通过将热能转换为动能而不是应变能来解决这一限制。讨论了应变法和动能法之间的根本区别。结果表明,用动能方法预测的无约束热膨胀与连续统本构模型无关,因此,这种公式可以用于固体和流体。讨论了位移(动力学)和应变(应力)公式,从宏观上阐明了热膨胀的机理。采用热膨胀位移公式(TEDF)和位置梯度乘分解法计算了由于边界和运动约束(BMC)引起的热应力。讨论了TEDF的实现问题,并在应用扫描矩阵技术消除刚体热位移平移模式后确定了预处理阶段的常数矩阵。此外,在高温下,研究了由于本构模型依赖于温度而产生的软化效应。数值结果显示了将热能转化为动能的TEDF方法与将热能转化为产生弹性应力的应变能的传统有限元方法之间的根本区别。
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来源期刊
CiteScore
4.00
自引率
10.00%
发文量
72
审稿时长
6-12 weeks
期刊介绍: The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.
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