finite element formulation meaning in English
有限单元公式
Examples
- Abstract : this paper presents the finite element formulation of frame structures with distributed piezoelectric sensors and actuators . the piezoelectric stiffness matrix and dielectric stiffness matrix of a frame element are derived . a numerical example is given to illustrate the application of piezoelectric sensors and actuators in structure vibration control by implementing two fundamental control laws
文摘:重点阐述了含压电传感器和执行器的复合结构框架有限元模型的建立过程,导出了压电框架单元的压电刚度矩阵和介电刚度矩阵;进而引入基本控制规律用数值例子说明了压电传感器与执行器在结构的振动控制中的具体应用。 - For the boundary - value problem , such as dynamic response of seabed , the finite element formulations of u ~ u and u ~ p forms of generalized biot ' s theory are established in this dissertation . usually the direct solution of u ~ p form is viewed as rather difficult . a procedure is developed by the author
本文针对海床动力响应边值问题，推导了广义biot理论u u和u p两种形式的有限元列式，实现了通常认为很困难的u p形式直接解法，并将交叉迭代法扩展至两种u p形式的综合求解。 - In this paper , at the cut - in spot of beam active vibration control and use the pzt material as the drive component , the main research works can be summarized as follows : 1 ) using the finite element theory , a general finite element formulation of piezoelectric media is derived , the direct and converse piezoelectric effects are considered in the formulation
本文从梁的振动主动控制研究为切入点，利用了pzt材料作为驱动元件，作了如下几个方面的研究： 1 )利用有限元理论，考虑压电材料的正、逆压电效应的影响，导出了机电耦合压电元件的有限元方程。 - Eigenequation about singularity , singular stress fields and electrical displacement fields near the interface edge are obtained under axisymmetric distortion . finally , a special finite element formulation which is based on the principle of minimum potential energy has been developed for determining the orders of the singularity of the singular stress fields around the singular point ( interface edge , interface corner and the interface crack ) in the bonded dissimilar anisotropic / anisotropic , piezoelectric / piezoelectric as well as piezoelectric / anisotropic materials . the numerical results show that this method is very convenient and efficient
最后，从最小势能原理出发，在仅仅考虑奇异性支配区域这一前提下，对于弹性接合材料的平面变形问题和拟平面应变问题，以奇异点为原点分别建立极坐标系和圆柱坐标系，通过分部积分消除厂项，从而使奇异性问题的求解由原来的二维降为一维；对于三维变形问题，以奇异点为原点建立球坐标系，通过分部积分消除项，从而使奇异性问题的求解由原来的三维降为二维。 - At first , the finite element formulation is presented to determine the flutter characteristics of laminated panels at elevated temperature . then both the linear and nonlinear panel flutter characteristics are analyzed . the panel flutter boundaries are finally determined and the effect of temperature , airflow speed , etc , on the panel flutter characteristics is analyzed
为此，本文首先建立了复合材料壁板热颤振的有限元模型并对受热壁板的线性和非线性颤振特性进行了研究；最后确定了壁板的颤振边界，分析了温度、来流速度等因素对壁板颤振特性的影响规律。