功能梯度材料板热传导及热弹性研究
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摘要
功能梯度材料由于其内部特殊的性能得到了广泛的应用。本文介绍了功能梯度材料热传导及热弹性问题的国内外研究现状和进展,将混合数值法和条单元法应用于功能梯度材料板的热传导及热弹性问题研究中,拓广了两种方法的应用领域,为研究功能梯度材料的热问题提供了一种新途径。
混合数值法已经广泛应用于复合层板的位移响应研究中,本文在此基础上将此方法应用于功能梯度材料板的热传导问题研究,推导了混合数值法的热传导公式。从功能梯度材料板的热平衡方程出发,在问题域的不同方向采用不同的理论方法,通过求解能量形式的加权残值方程得到了热传导问题的解。并应用于由陶瓷ZrO 2和金属Ti-6Al-4V两种材料合成且沿板厚方向物性参数呈连续线性变化的功能梯度材料板的热传导问题。分析了热源为持续作用与瞬时作用两种情况下的热传导,得到了功能梯度板在不同时刻及不同位置的温度分布状况。将混合数值法应用于热传导分析中,扩大了此方法的应用领域,为研究热传导问题开辟了新思路。
文中还采用混合数值法研究了功能梯度材料板的热弹性问题,推导了混合数值法的热弹性公式。从功能梯度材料板的平衡方程出发,在问题域的不同方向采用不同的理论方法,通过求解能量形式的虚功原理方程得到了热弹性问题的位移响应解。用此方法分析了由不锈钢和氮化硅两种材料合成且沿板厚方向物性参数呈连续线性变化的功能梯度材料板的热弹性问题。并针对温度变化热源为持续作用与瞬时作用两种状态进行热弹性分析,得到了功能梯度板在不同时刻及不同位置的位移响应,并进一步考察了功能梯度板中的应力波。混合数值法应用于热弹性问题中,是在热传导分析基础上的进一步深入,为热弹性响应问题的研究提供了新思路。
本文将条单元法法应用于功能梯度材料热弹性问题的研究中。从基本平衡方程出发,系统推导了条单元法的热弹性问题的公式,通过求解能量形式的虚功原理方程得到热弹性问题的通解,通解由齐次方程解和特解两部分构成。采用条单元法分析了无限大功能梯度材料板热弹性问题,给出了功能梯度板的热弹性响应分布,文中还分别采用混合数值法和条单元法对同一热弹性问题进行了比较分析,通过改变人为边界条件的位置验证了连接边界条件的正确性。
文中还采用条单元法研究了带竖向裂缝和横向裂缝的功能梯度板热弹性位移响应问题,通过研究功能梯度板上出现的位移响应,指出了不同性质的裂缝对热弹性位移响应的影响,并通过改变裂缝距离热源的位置、改变裂缝的长度及改变热源频率等情况下,对功能梯度板上出现热弹性位移响应进行了深入的分析。同时提出了通过热弹性位移响应特性来识别材料中出现裂缝及有关裂缝特性的方法,当系统不能通过外力响应方式进行无损检测时,可以考虑采用热弹性响应方法进行检测。
Functionally Graded Material (FGM) is widely used for its special performance. In this dissertation, the recent developments of Functionally Graded Material about heat problems are briefly summarized. Hybrid Numerical Method (HNM) and Strip Element Method (SEM) are applied to heat conduction and thermoelastic problems of FGM plates. This is the extension and exploitation for two methods and provided a new way for investigating heat effect of FGM plates.
The HNM has been widely applied into the displacement response of composite laminated plates. We apply HNM into heat conduction analysis of FGM plates. The formula of heat conduction of HNM is deduced. On the basic of heat balance equation of FGM plates, different methods are used in the different directions. The solutions of heat conduction problems are obtained by method of weighted residual. Using HNM the Heat conduction problem of FGM plates, been composite of ceramic material ZrO 2and metal material Ti-6Al-4V , are analysed. The material properties of the FGM plates are assumed to vary linearly in the thickness direction. Heat conduction of the plates is analysed for continuous action and transient action of the heat source and the temperature distributions of FGM plates in different time and different position are obtained. The HNM applied to heat conduction not only extends the application region of this method but also provide a new study way for heat conduction problems.
HNM is further applied into thermoelastic analysis of FGM plates. The thermoelastic formula of HNM is deduced. On the basic of balance equation of FGM plates, Different methods are used in the different directions. The solutions of thermoelastic problems are obtained by the principle of virtual work. Using HNM thermoelastic problems of FGM plates, been composite of stainless steel and silicon nitride, are analysed. The material properties of the FGM plates are assumed to vary linearly in the thickness direction. The thermoelastic problems are analysed for continuous action and transient action of temperature change source. The displacement responses of FGM plates in different time and different position are obtained and stress wave are also investigated. Applying HNM into thermoelastic problems is further studying based on heat conduction and provides a new way for studying the thermoelastic response.
SEM is developed on the basic of HNM. The SEM has been widely applied into the displacement response of composite laminated plates. SEM is applied into thermoelastic problems of FGM on the basic of ever done. On the basic of balance equation, the formula of thermoelastic problems of SEM is deduced. The general solution of thermoelastic problem is obtained by the principle of virtual work. The general solution is formed by two parts: particular solution and complementary solution.Thermoelastic problems of infinite FGM plates are analysed using SEM. The thermoelastic response distributions of FGM plates are obtained. The same thermoelastic problem is analysed using HNM and SEM, respectively. The connection boundary conditions have been verified correctly by varying different connection position.
The thermoelastic problems of FGM plates with horizontal cracks and vertical cracks are also investigated using SEM. The influence of different character cracks to the thermoelastic response is investigated by studying the displacement response. Different thermoelastic response are deeply analysed by considering different conditions, such as, varying the distance of cracks from heat source, different length of crack and different frequency of heat source. The method of identifying the character of cracks by investigating thermoelastic displacement response is proposed. Thermoelastic response method can be used to detect the character of the system while it has difficulty to apply force response to the system.
混合数值法已经广泛应用于复合层板的位移响应研究中,本文在此基础上将此方法应用于功能梯度材料板的热传导问题研究,推导了混合数值法的热传导公式。从功能梯度材料板的热平衡方程出发,在问题域的不同方向采用不同的理论方法,通过求解能量形式的加权残值方程得到了热传导问题的解。并应用于由陶瓷ZrO 2和金属Ti-6Al-4V两种材料合成且沿板厚方向物性参数呈连续线性变化的功能梯度材料板的热传导问题。分析了热源为持续作用与瞬时作用两种情况下的热传导,得到了功能梯度板在不同时刻及不同位置的温度分布状况。将混合数值法应用于热传导分析中,扩大了此方法的应用领域,为研究热传导问题开辟了新思路。
文中还采用混合数值法研究了功能梯度材料板的热弹性问题,推导了混合数值法的热弹性公式。从功能梯度材料板的平衡方程出发,在问题域的不同方向采用不同的理论方法,通过求解能量形式的虚功原理方程得到了热弹性问题的位移响应解。用此方法分析了由不锈钢和氮化硅两种材料合成且沿板厚方向物性参数呈连续线性变化的功能梯度材料板的热弹性问题。并针对温度变化热源为持续作用与瞬时作用两种状态进行热弹性分析,得到了功能梯度板在不同时刻及不同位置的位移响应,并进一步考察了功能梯度板中的应力波。混合数值法应用于热弹性问题中,是在热传导分析基础上的进一步深入,为热弹性响应问题的研究提供了新思路。
本文将条单元法法应用于功能梯度材料热弹性问题的研究中。从基本平衡方程出发,系统推导了条单元法的热弹性问题的公式,通过求解能量形式的虚功原理方程得到热弹性问题的通解,通解由齐次方程解和特解两部分构成。采用条单元法分析了无限大功能梯度材料板热弹性问题,给出了功能梯度板的热弹性响应分布,文中还分别采用混合数值法和条单元法对同一热弹性问题进行了比较分析,通过改变人为边界条件的位置验证了连接边界条件的正确性。
文中还采用条单元法研究了带竖向裂缝和横向裂缝的功能梯度板热弹性位移响应问题,通过研究功能梯度板上出现的位移响应,指出了不同性质的裂缝对热弹性位移响应的影响,并通过改变裂缝距离热源的位置、改变裂缝的长度及改变热源频率等情况下,对功能梯度板上出现热弹性位移响应进行了深入的分析。同时提出了通过热弹性位移响应特性来识别材料中出现裂缝及有关裂缝特性的方法,当系统不能通过外力响应方式进行无损检测时,可以考虑采用热弹性响应方法进行检测。
Functionally Graded Material (FGM) is widely used for its special performance. In this dissertation, the recent developments of Functionally Graded Material about heat problems are briefly summarized. Hybrid Numerical Method (HNM) and Strip Element Method (SEM) are applied to heat conduction and thermoelastic problems of FGM plates. This is the extension and exploitation for two methods and provided a new way for investigating heat effect of FGM plates.
The HNM has been widely applied into the displacement response of composite laminated plates. We apply HNM into heat conduction analysis of FGM plates. The formula of heat conduction of HNM is deduced. On the basic of heat balance equation of FGM plates, different methods are used in the different directions. The solutions of heat conduction problems are obtained by method of weighted residual. Using HNM the Heat conduction problem of FGM plates, been composite of ceramic material ZrO 2and metal material Ti-6Al-4V , are analysed. The material properties of the FGM plates are assumed to vary linearly in the thickness direction. Heat conduction of the plates is analysed for continuous action and transient action of the heat source and the temperature distributions of FGM plates in different time and different position are obtained. The HNM applied to heat conduction not only extends the application region of this method but also provide a new study way for heat conduction problems.
HNM is further applied into thermoelastic analysis of FGM plates. The thermoelastic formula of HNM is deduced. On the basic of balance equation of FGM plates, Different methods are used in the different directions. The solutions of thermoelastic problems are obtained by the principle of virtual work. Using HNM thermoelastic problems of FGM plates, been composite of stainless steel and silicon nitride, are analysed. The material properties of the FGM plates are assumed to vary linearly in the thickness direction. The thermoelastic problems are analysed for continuous action and transient action of temperature change source. The displacement responses of FGM plates in different time and different position are obtained and stress wave are also investigated. Applying HNM into thermoelastic problems is further studying based on heat conduction and provides a new way for studying the thermoelastic response.
SEM is developed on the basic of HNM. The SEM has been widely applied into the displacement response of composite laminated plates. SEM is applied into thermoelastic problems of FGM on the basic of ever done. On the basic of balance equation, the formula of thermoelastic problems of SEM is deduced. The general solution of thermoelastic problem is obtained by the principle of virtual work. The general solution is formed by two parts: particular solution and complementary solution.Thermoelastic problems of infinite FGM plates are analysed using SEM. The thermoelastic response distributions of FGM plates are obtained. The same thermoelastic problem is analysed using HNM and SEM, respectively. The connection boundary conditions have been verified correctly by varying different connection position.
The thermoelastic problems of FGM plates with horizontal cracks and vertical cracks are also investigated using SEM. The influence of different character cracks to the thermoelastic response is investigated by studying the displacement response. Different thermoelastic response are deeply analysed by considering different conditions, such as, varying the distance of cracks from heat source, different length of crack and different frequency of heat source. The method of identifying the character of cracks by investigating thermoelastic displacement response is proposed. Thermoelastic response method can be used to detect the character of the system while it has difficulty to apply force response to the system.
引文
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