电子设备动态性能有限元建模与优化方法研究
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摘要
电子设备是现代工农业生产和人们日常生活中不可或缺的工具设备。随着电子设备向集成化、专业化和精密化方向发展,对结构动态性能的要求也越来越高。而电子设备结构动态性能分析与优化是现代电子设备结构性能评估和性能改进的重要方式。本论文针对电子设备结构动态性能有限元建模与优化中所面临的问题,进行了如下研究。
1)电子设备子结构建模方法研究
首先,提出了参数化子结构建模方法。该方法在实现对同类结构分析建模的同时,可大大减少建模工作量。其次,利用Numman级数和摄动理论分析了静力凝聚动态子结构方法中因自由度凝聚而产生的误差,并利用板状结构实例对主自由度的选择策略进行了对比分析研究,分析结论和理论分析吻合。
2)PCB板动态性能等效建模方法研究
首先,提出了基于有限元模型的PCB板动态性能等效建模方法。该方法利用原PCB板的几何主尺寸作为等效板的几何尺寸,采用单一均匀材料替代原材料,利用质量相等原则获得等效板的等效密度,并利用有限元理论和振动理论推导了基于有限元模型的等效刚度计算方法。同时分析了元器件质量和刚度对等效刚度的影响。其次,针对有限元建模困难或无法进行建模的复杂PCB板,提出了基于实验数据的PCB动态性能等效建模方法,并利用有限元理论和振动理论推导了等效刚度计算方法,同时分析了电子器件的支撑方式对等效刚度的影响。
3)PCB板最大频率支撑布局拓扑优化方法研究
基于PCB板支撑结构的特点,建立了最大频率支撑布局拓扑优化方法:利用无质量实体单元模拟支撑部分;利用自由度凝聚技术建立PCB板及其元器件的子结构模型,从而大大缩减了优化的计算量;利用渐进优化方法推导出结构支撑单元的删除敏度并建立了基于ANSYS的计算方法,并分析了支撑刚度对支撑布局优化的影响。最后通过实例验证了优化方法的正确性。
4)PCB板动态性能优化方法研究
首先,利用自由度凝聚技术和模态综合方法,建立面向元器件的PCB动态性能布局优化方法。在优化模型的求解上,考虑元器件之间的几何干涉问题,提出改进的遗传算法。其次,结合动态子结构建模分析方法和遗传算法,建立了PCB板支撑布局的优化方法,对支撑位置与PCB板节点不重合问题进行了研究,并结合ANSYS二次开发技术和遗传算法开发了求解程序。
5)电子设备结构有限元分析优化软件实现方法研究
针对电子设备结构分析优化软件实现中所面临的问题,建立了面向对象的二次开发软件实现方法。该方法可充分利用有限元分析软件资源,不需要进行有限元底层算法程序开发,开发效率高,且计算结果可得到保证。同时该方法采用了面向对象的思想,因而程序设计思路清晰,调试容易。
论文取得的主要的创新成果如下。
1)提出了一种基于有限元模型的PCB板等效建模方法
针对含有复杂PCB板的电子设备结构动态性能分析,提出了一种基于有限元模型的PCB板等效建模方法。该方法利用原PCB板的几何主尺寸作为等效板的几何尺寸,采用单一均匀材料替代原材料,利用质量相等原则获得等效板的等效密度,并利用有限元理论和振动理论推导了等效刚度计算方法。最后分析了元器件质量和刚度对等效刚度的影响。
2)提出了一种基于实验数据的PCB板动态性能等效方法
复杂PCB板,由于很难获得板上电子元器件的结构材料参数和结构形式,导致有限元建模比较困难或无法进行有限元建模。为此,提出了一种基于实验数据的PCB板动态性能等效建模方法。该方法利用原PCB板的几何主尺寸作为等效模型的几何尺寸,采用单一均匀材料替代原材料,利用质量相等原则获得等效模型的等效密度,在并利用有限元理论和振动理论对推导了等效刚度计算方法。最后分析了PCB板的支撑方式对等效刚度的影响,并利用实例计算验证了该方法的可行性能和正确性。
3)建立了PCB板最大频率支撑布局拓扑优化方法
PCB板的支持布局会影响其刚度分布,进而影响结构的模态频率。为此,建立了PCB板最大频率支撑拓扑优化方法。该方法利用自由度凝聚方法缩减优化模型计算量,利用渐进优化方法推导了单元删除敏度,并研究建立了基于ANSYS的计算实现方法。最后分析了支撑材料刚度对支撑拓扑优化的影响,并通过两个个优化实例验证了该方法的正确性。
Electronic devices are indispensable to modern industry, agriculture as well as our daily life. Along with the development of electronic devices towards integration, specialization and high accuracy, requirements on their structural dynamic properties have been continuously increasing. Thus the related analysis and optimization based on finite element method (FEM) are now playing more and more important roles in the evaluation and improvement of the structural performance of electronic devices. According to the problems in structural analysis and optimization of electronic devices, this thesis focuses on the researches shown as follows.
1) Study of substructure modeling method in structural analysis of electronic devices
Firstly, a parametric substructure method is presented, which enables convenient modeling and analysis for homogeneous structures while significantly reduces its human labors. Secondly, the causes of the error in static condensation substructure method are deduced based on Numman series and matrix perturbation theory. Additionally, comparisons among some strategies for selection of master degree of freedom (MDOF) in plate-like structure are also made in the thesis, which shows good consistency with the theoretical conclusions.
2) Study of equivalent method for modeling of printed circuit board (PCB) dynamic properties
Firstly, an equivalent method for modeling of PCB dynamic properties based on FEM is presented. In the method, equivalent dimensions are obtained from the main dimension of a real PCB, while equivalent density is calculated by the principle of mass equality, and the equivalent stiffness formula is derived based on vibration theory and FEM, respectively. The effects of size, location and layout of components on equivalent stiffness are discussed. For the complex PCB of which FEM modeling is too difficult, an equivalent modeling method based on experiment data about PCB dynamic properties is also presented, in which equivalent stiffness is derived based on vibration theory and FEM. Additionally, the influence of the support condition on equivalent stiffness is discussed as well.
3) Study of maximization of PCB natural frequency by optimization of supporting layout
Based on the structural characters of PCB, a topology optimization method of PCB structure is established. In this method the supporting part is simulated by elastic material with no mass, and the PCB component part is refined by condensation of degree of freedom to reduce computation amount. The sensitivity coefficient for element removal is derived by evolutionary structural optimization (ESO) algorithm. And then, an ANSYS-based computational method is presented. Meanwhile, the influence of stiffness of support material on the maximal frequency of structure is discussed. In the end, optimization examples demonstrate that this method is reasonable and effective in engineering projects.
4) Study of PCB dynamical property optimization method
Firstly, by using freedom condensing technology and modal synthesis method, a new component layout optimization method is presented for PCB dynamic properties. By using a modified genetic algorithm, the layout optimization problem for multiple components can be solved. And then, a new support layout optimization method for PCB structure is built up. Additionally, by using the genetic algorithm and second-develop technique, a solving software developed.
5) Study of software development method for structural analysis and optimization of electric devices
To resolve the problems of complexity and ineffectiveness in FEM modeling, an object oriented secondary development method is presented. By taking full advantage of the resource of FEM software, the method avoids development of fundamental FEM algorithm, and thus leads to a high development efficiency as well as good reliability. Besides, by using the object-oriented theory, the program design thought is much clearer and the debugging is much easier.
The originalities in this thesis can be summarized as follows:
1) An equivalent method for modeling of PCB dynamic properties based on FEM model is presented
In the method, the equivalent dimension is obtained from the main dimension of real PCB, the equivalent density is calculated by the principle of mass equality, and the equivalent stiffness formula is derived based on the theory of vibration and finite element method. Additionally, the influences of the size, the location and the layout of part on equivalent stiffness are studied.
2) An equivalent method for modeling of PCB dynamic properties based on experimental data is proposed
Finite-element modeling of PCB is often very difficulty due to the structural complexity, so an equivalent modeling method of PCB based on experimental data for dynamic property analysis is presented. In the method, the equivalent dimension is obtained from main dimension of real PCB structure, the equivalent density is calculated by the principle of mass equality, and the equivalent stiffness formula is derived based on the theory of vibration and finite element method. Additionally, the influences of joint constrain on equivalent stiffness are studied.
3) A PCB dynamical property layout optimization method is built up
Support layout will affect the stiffness distribution of PCB, and then affect the modal frequency. The method of maximization of PCB natural frequency with optimal support layout is built up. Using condensation method of degree of freedom for reduce computation amount. And the sensitivity number for element removal is derived by using evolutionary structural optimization algorithm and the implementation method by using ANSYS is built up. In the end, the influences of support material stiffness on the maximal frequency of structure are discussed. Application examples show the optimization method is effective and efficient in engineering projects.
1)电子设备子结构建模方法研究
首先,提出了参数化子结构建模方法。该方法在实现对同类结构分析建模的同时,可大大减少建模工作量。其次,利用Numman级数和摄动理论分析了静力凝聚动态子结构方法中因自由度凝聚而产生的误差,并利用板状结构实例对主自由度的选择策略进行了对比分析研究,分析结论和理论分析吻合。
2)PCB板动态性能等效建模方法研究
首先,提出了基于有限元模型的PCB板动态性能等效建模方法。该方法利用原PCB板的几何主尺寸作为等效板的几何尺寸,采用单一均匀材料替代原材料,利用质量相等原则获得等效板的等效密度,并利用有限元理论和振动理论推导了基于有限元模型的等效刚度计算方法。同时分析了元器件质量和刚度对等效刚度的影响。其次,针对有限元建模困难或无法进行建模的复杂PCB板,提出了基于实验数据的PCB动态性能等效建模方法,并利用有限元理论和振动理论推导了等效刚度计算方法,同时分析了电子器件的支撑方式对等效刚度的影响。
3)PCB板最大频率支撑布局拓扑优化方法研究
基于PCB板支撑结构的特点,建立了最大频率支撑布局拓扑优化方法:利用无质量实体单元模拟支撑部分;利用自由度凝聚技术建立PCB板及其元器件的子结构模型,从而大大缩减了优化的计算量;利用渐进优化方法推导出结构支撑单元的删除敏度并建立了基于ANSYS的计算方法,并分析了支撑刚度对支撑布局优化的影响。最后通过实例验证了优化方法的正确性。
4)PCB板动态性能优化方法研究
首先,利用自由度凝聚技术和模态综合方法,建立面向元器件的PCB动态性能布局优化方法。在优化模型的求解上,考虑元器件之间的几何干涉问题,提出改进的遗传算法。其次,结合动态子结构建模分析方法和遗传算法,建立了PCB板支撑布局的优化方法,对支撑位置与PCB板节点不重合问题进行了研究,并结合ANSYS二次开发技术和遗传算法开发了求解程序。
5)电子设备结构有限元分析优化软件实现方法研究
针对电子设备结构分析优化软件实现中所面临的问题,建立了面向对象的二次开发软件实现方法。该方法可充分利用有限元分析软件资源,不需要进行有限元底层算法程序开发,开发效率高,且计算结果可得到保证。同时该方法采用了面向对象的思想,因而程序设计思路清晰,调试容易。
论文取得的主要的创新成果如下。
1)提出了一种基于有限元模型的PCB板等效建模方法
针对含有复杂PCB板的电子设备结构动态性能分析,提出了一种基于有限元模型的PCB板等效建模方法。该方法利用原PCB板的几何主尺寸作为等效板的几何尺寸,采用单一均匀材料替代原材料,利用质量相等原则获得等效板的等效密度,并利用有限元理论和振动理论推导了等效刚度计算方法。最后分析了元器件质量和刚度对等效刚度的影响。
2)提出了一种基于实验数据的PCB板动态性能等效方法
复杂PCB板,由于很难获得板上电子元器件的结构材料参数和结构形式,导致有限元建模比较困难或无法进行有限元建模。为此,提出了一种基于实验数据的PCB板动态性能等效建模方法。该方法利用原PCB板的几何主尺寸作为等效模型的几何尺寸,采用单一均匀材料替代原材料,利用质量相等原则获得等效模型的等效密度,在并利用有限元理论和振动理论对推导了等效刚度计算方法。最后分析了PCB板的支撑方式对等效刚度的影响,并利用实例计算验证了该方法的可行性能和正确性。
3)建立了PCB板最大频率支撑布局拓扑优化方法
PCB板的支持布局会影响其刚度分布,进而影响结构的模态频率。为此,建立了PCB板最大频率支撑拓扑优化方法。该方法利用自由度凝聚方法缩减优化模型计算量,利用渐进优化方法推导了单元删除敏度,并研究建立了基于ANSYS的计算实现方法。最后分析了支撑材料刚度对支撑拓扑优化的影响,并通过两个个优化实例验证了该方法的正确性。
Electronic devices are indispensable to modern industry, agriculture as well as our daily life. Along with the development of electronic devices towards integration, specialization and high accuracy, requirements on their structural dynamic properties have been continuously increasing. Thus the related analysis and optimization based on finite element method (FEM) are now playing more and more important roles in the evaluation and improvement of the structural performance of electronic devices. According to the problems in structural analysis and optimization of electronic devices, this thesis focuses on the researches shown as follows.
1) Study of substructure modeling method in structural analysis of electronic devices
Firstly, a parametric substructure method is presented, which enables convenient modeling and analysis for homogeneous structures while significantly reduces its human labors. Secondly, the causes of the error in static condensation substructure method are deduced based on Numman series and matrix perturbation theory. Additionally, comparisons among some strategies for selection of master degree of freedom (MDOF) in plate-like structure are also made in the thesis, which shows good consistency with the theoretical conclusions.
2) Study of equivalent method for modeling of printed circuit board (PCB) dynamic properties
Firstly, an equivalent method for modeling of PCB dynamic properties based on FEM is presented. In the method, equivalent dimensions are obtained from the main dimension of a real PCB, while equivalent density is calculated by the principle of mass equality, and the equivalent stiffness formula is derived based on vibration theory and FEM, respectively. The effects of size, location and layout of components on equivalent stiffness are discussed. For the complex PCB of which FEM modeling is too difficult, an equivalent modeling method based on experiment data about PCB dynamic properties is also presented, in which equivalent stiffness is derived based on vibration theory and FEM. Additionally, the influence of the support condition on equivalent stiffness is discussed as well.
3) Study of maximization of PCB natural frequency by optimization of supporting layout
Based on the structural characters of PCB, a topology optimization method of PCB structure is established. In this method the supporting part is simulated by elastic material with no mass, and the PCB component part is refined by condensation of degree of freedom to reduce computation amount. The sensitivity coefficient for element removal is derived by evolutionary structural optimization (ESO) algorithm. And then, an ANSYS-based computational method is presented. Meanwhile, the influence of stiffness of support material on the maximal frequency of structure is discussed. In the end, optimization examples demonstrate that this method is reasonable and effective in engineering projects.
4) Study of PCB dynamical property optimization method
Firstly, by using freedom condensing technology and modal synthesis method, a new component layout optimization method is presented for PCB dynamic properties. By using a modified genetic algorithm, the layout optimization problem for multiple components can be solved. And then, a new support layout optimization method for PCB structure is built up. Additionally, by using the genetic algorithm and second-develop technique, a solving software developed.
5) Study of software development method for structural analysis and optimization of electric devices
To resolve the problems of complexity and ineffectiveness in FEM modeling, an object oriented secondary development method is presented. By taking full advantage of the resource of FEM software, the method avoids development of fundamental FEM algorithm, and thus leads to a high development efficiency as well as good reliability. Besides, by using the object-oriented theory, the program design thought is much clearer and the debugging is much easier.
The originalities in this thesis can be summarized as follows:
1) An equivalent method for modeling of PCB dynamic properties based on FEM model is presented
In the method, the equivalent dimension is obtained from the main dimension of real PCB, the equivalent density is calculated by the principle of mass equality, and the equivalent stiffness formula is derived based on the theory of vibration and finite element method. Additionally, the influences of the size, the location and the layout of part on equivalent stiffness are studied.
2) An equivalent method for modeling of PCB dynamic properties based on experimental data is proposed
Finite-element modeling of PCB is often very difficulty due to the structural complexity, so an equivalent modeling method of PCB based on experimental data for dynamic property analysis is presented. In the method, the equivalent dimension is obtained from main dimension of real PCB structure, the equivalent density is calculated by the principle of mass equality, and the equivalent stiffness formula is derived based on the theory of vibration and finite element method. Additionally, the influences of joint constrain on equivalent stiffness are studied.
3) A PCB dynamical property layout optimization method is built up
Support layout will affect the stiffness distribution of PCB, and then affect the modal frequency. The method of maximization of PCB natural frequency with optimal support layout is built up. Using condensation method of degree of freedom for reduce computation amount. And the sensitivity number for element removal is derived by using evolutionary structural optimization algorithm and the implementation method by using ANSYS is built up. In the end, the influences of support material stiffness on the maximal frequency of structure are discussed. Application examples show the optimization method is effective and efficient in engineering projects.
引文
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