CN111783348A - Calculation method for centroid drift of variable-thickness shell element based on finite element analysis - Google Patents
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Abstract
Description
技术领域technical field
本发明属于结构有限元分析领域，涉及基于有限元分析的变厚度壳单元质心漂移量计算方法。The invention belongs to the field of structural finite element analysis, and relates to a method for calculating the drift of the centroid of a variable-thickness shell element based on the finite element analysis.
背景技术Background technique
三轴气浮台是航天器姿态控制系统全物理仿真的核心设备，地面采用大型三轴气浮台进行物理仿真时，气浮台结构变形导致整体质心的微小偏移，该微偏移量会导致重力对三轴气浮台产生一个干扰力矩。该干扰力矩的大小能否满足技术指标是决定设计成败的关键技术之一，10t三轴气浮台要求空载下干扰力矩优于0.01N·m，大惯量下干扰力矩优于0.02N·m。The three-axis air flotation stage is the core equipment for the full physical simulation of the spacecraft attitude control system. When a large three-axis air flotation stage is used on the ground for physical simulation, the deformation of the air flotation stage leads to a slight offset of the overall center of mass. This causes gravity to produce an interference moment on the triaxial air flotation table. Whether the size of the interference torque can meet the technical indicators is one of the key technologies to determine the success or failure of the design. The 10t triaxial air-floating table requires the interference torque to be better than 0.01N·m under no-load, and better than 0.02N·m under large inertia. .
精确计算出三轴气浮台结构转动到任意角度重力导致质心的漂移量非常重要，使用 abaqus软件可以直接得到变形前结构质心位置，通过导入计算结果odb文件可以获得变形后结构，赋予材料属性后即可得到变形后结构质心，然而abaqus软件无法获得变厚度壳单元的质量属性，三轴气浮台有限元模型中涉及到变厚度的壳单元无法通过有限元软件abaqus直接提取变形前后质心位置。It is very important to accurately calculate the drift of the center of mass caused by the rotation of the triaxial air-floating table structure to any angle due to gravity. Using the abaqus software, the position of the center of mass of the structure before deformation can be directly obtained, and the deformed structure can be obtained by importing the calculation result odb file. The center of mass of the deformed structure can be obtained. However, the mass properties of the variable-thickness shell element cannot be obtained by the abaqus software. The variable-thickness shell element in the finite element model of the triaxial air-floating table cannot directly extract the position of the center of mass before and after the deformation through the finite element software abaqus.
经过对现有技术的检索，只公开了三角形单元和四面体单元质心漂移的计算方法，没有涉及到变厚度壳单元质心漂移计算方法，也公开了通过有限元软件MSC Patran的二次开发计算变形体质心漂移，但没有具体给出计算方法和对变厚度壳单元质心漂移的计算。After searching the prior art, only the calculation method of the centroid drift of the triangular element and the tetrahedral element is disclosed, and the calculation method of the centroid drift of the variable-thickness shell element is not involved. Body centroid drift, but no specific calculation method and calculation of centroid drift for variable thickness shell elements are given.
发明内容SUMMARY OF THE INVENTION
本发明要解决的问题是在于提供基于有限元分析的变厚度壳单元质心漂移量计算方法，横向刚度得到了加强，降低气浮台干扰力矩。The problem to be solved by the present invention is to provide a method for calculating the drift of the center of mass of a variable-thickness shell element based on finite element analysis, the lateral rigidity is strengthened, and the disturbance moment of the air-floating table is reduced.
为解决上述技术问题，本发明采用的技术方案是：基于有限元分析的变厚度壳单元质心漂移量计算方法，包括以下步骤，In order to solve the above-mentioned technical problems, the technical solution adopted in the present invention is: a method for calculating the drift amount of the center of mass of a variable-thickness shell element based on finite element analysis, comprising the following steps:
S1、建立变厚度属性的壳截面，壳截面厚度为空间坐标的函数f(x,y,z,δ)＝0，对具有壳属性的几何模型分配变厚度截面属性，基于几何模型划分网格，设定边界条件，提交计算；S1. Establish a shell section with variable thickness attribute. The thickness of the shell section is a function of space coordinates f(x, y, z, δ) = 0, assign the variable thickness section attribute to the geometric model with the shell attribute, and divide the mesh based on the geometric model. , set the boundary conditions, and submit the calculation;
S2、建立二次开发程序，提取变形前网格节点，将四边形单元离散成三角形单元；S2. Establish a secondary development program, extract the mesh nodes before deformation, and discretize the quadrilateral elements into triangular elements;
S3、建立局部坐标系O'X'Y'Z'，取三角形长边为局部坐标系X'轴，长边的高所在的轴作为局部坐标系Y'轴，Z'轴按照右手定则确定；S3. Establish a local coordinate system O'X'Y'Z', take the long side of the triangle as the X' axis of the local coordinate system, the axis where the height of the long side is located as the Y' axis of the local coordinate system, and the Z' axis is determined according to the right-hand rule ;
S4、建立局部坐标系和整体坐标系的坐标转换矩阵M1，获取局部坐标系下壳截面厚度随空间坐标变化的函数g(x',y',z',δ)＝0；S4, establish the coordinate transformation matrix M1 of the local coordinate system and the global coordinate system, and obtain the function g(x', y', z', δ)=0 of the thickness of the shell section under the local coordinate system changing with the spatial coordinates;
S5、局部坐标系下对三角形单元进行积分，获得三角形单元的体积，结合材料密度获取三角形单元质量和局部坐标系下质心位置，根据坐标转换矩阵获得三角形单元在整体坐标系下质心位置，应用质心公式计算变形前结构整体质心；S5. Integrate the triangular element in the local coordinate system to obtain the volume of the triangular element, obtain the mass of the triangular element and the position of the centroid in the local coordinate system in combination with the material density, obtain the centroid position of the triangular element in the global coordinate system according to the coordinate transformation matrix, and apply the centroid The formula calculates the overall center of mass of the structure before deformation;
S6、按照步骤2的方法将变形后的四边形单元离散成三角形单元，按照步骤3的方法确定变形后三角形单元的局部坐标系O"X"Y"Z"；S6. Discrete the deformed quadrilateral unit into triangular units according to the method of step 2, and determine the local coordinate system O"X"Y"Z" of the deformed triangular unit according to the method of step 3;
S7、应用空间距离公式计算变形前后质心漂移量。S7. Calculate the displacement of the center of mass before and after the deformation by applying the spatial distance formula.
进一步的，在步骤S4中，坐标转换矩阵表述如下：Further, in step S4, the coordinate transformation matrix is expressed as follows:
将f(x,y,z,δ)＝0中的x、y、z参数通过坐标转换矩阵用x'、y'、z'代替，即得到局部坐标系下的壳厚度空间分布函数g(x',y',z',δ)＝0。Replace the x, y, z parameters in f(x, y, z, δ)=0 with x', y', z' through the coordinate transformation matrix, that is, the shell thickness spatial distribution function g( x', y', z', δ)=0.
进一步的，在步骤S5中，局部坐标系下体积和质心公式如下：Further, in step S5, the formulas of volume and centroid in the local coordinate system are as follows:
进一步的，在步骤S6中，单元特征尺寸不大于结构特征尺寸1/50时，单个三角形单元尺寸变形与该三角形单元整体位移相比为高阶小量，认为变形后局部坐标系下三角形单元质量和质心位置与变形前相同，以步骤S5确定的变形前三角形单元质心位置坐标作为变形后三角形单元在局部坐标系的质心坐标，以步骤S5确定的变形前三角形单元质量作为变形后三角形单元质量，根据变形后单元局部坐标系和整体坐标系的坐标转换矩阵M2，计算变形后三角形单元在整体坐标系下的质心位置，根据质心公式得到变形后结构整体质心位置。Further, in step S6, when the unit feature size is not greater than 1/50 of the structural feature size, the size deformation of a single triangular unit is a high-order small amount compared with the overall displacement of the triangular unit, and it is considered that the quality of the triangular unit in the local coordinate system after deformation is The position of the centroid is the same as that before the deformation, and the position coordinates of the centroid of the triangular element before the deformation determined in step S5 are taken as the centroid coordinates of the triangular element after the deformation in the local coordinate system, and the mass of the triangular element before the deformation determined in step S5 is taken as the mass of the triangular element after the deformation, According to the coordinate transformation matrix M2 of the local coordinate system and the global coordinate system of the deformed element, the centroid position of the deformed triangular element in the global coordinate system is calculated, and the overall centroid position of the deformed structure is obtained according to the centroid formula.
进一步的，坐标转换矩阵表述如下，Further, the coordinate transformation matrix is expressed as follows,
进一步的，质心公式如下，Further, the centroid formula is as follows,
与现有技术相比，本发明具有的优点和积极效果如下。Compared with the prior art, the present invention has the following advantages and positive effects.
1、本发明横向刚度得到了加强，降低气浮台干扰力矩；1. The lateral rigidity of the present invention has been strengthened to reduce the interference moment of the air-floating table;
2、本发明拓展了质心偏移计算方法，对变厚度壳单元提供了高效精确的质心漂移计算方法，与体单元相比，大大节省有限元计算工作量；2. The present invention expands the calculation method of the centroid shift, provides an efficient and accurate calculation method for the centroid shift for the variable thickness shell element, and greatly saves the workload of finite element calculation compared with the body element;
3、本发明结合了有限元方法与数值计算方法，通过程序化方法可实现快速计算。3. The present invention combines the finite element method and the numerical calculation method, and can realize fast calculation through the programmed method.
附图说明Description of drawings
构成本发明的一部分的附图用来提供对本发明的进一步理解，本发明的示意性实施例及其说明用于解释本发明，并不构成对本发明的不当限定。在附图中：The accompanying drawings constituting a part of the present invention are used to provide further understanding of the present invention, and the exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the attached image:
图1是本发明三角形单元局部坐标系示意图；1 is a schematic diagram of a triangular element local coordinate system of the present invention;
图2是本发明变厚度圆筒模型；Fig. 2 is the variable thickness cylinder model of the present invention;
图3是本发明变厚度圆筒横截面。Figure 3 is a cross section of the variable thickness cylinder of the present invention.
具体实施方式Detailed ways
需要说明的是，在不冲突的情况下，本发明中的实施例及实施例中的特征可以相互组合。It should be noted that the embodiments of the present invention and the features of the embodiments may be combined with each other under the condition of no conflict.
在本发明的描述中，需要理解的是，术语“中心”、“纵向”、“横向”、“上”、“下”、“前”、“后”、“左”、“右”、“竖直”、“水平”、“顶”、“底”、“内”、“外”等指示的方位或位置关系为相对的方位或位置关系，仅是为了便于描述本发明和简化描述，而不是指示或暗示所指的装置或元件必须具有特定的方位、以特定的方位构造和操作，因此不能理解为对本发明的限制。此外，术语“第一”、“第二”等仅用于描述目的，而不能理解为指示或暗示相对重要性或者隐含指明所指示的技术特征的数量。由此，限定有“第一”、“第二”等的特征可以明示或者隐含地包括一个或者更多个该特征。在本发明的描述中，除非另有说明，“多个”的含义是两个或两个以上。In the description of the present invention, it should be understood that the terms "center", "portrait", "horizontal", "top", "bottom", "front", "rear", "left", "right", " The orientations or positional relationships indicated by vertical, horizontal, top, bottom, inner, and outer are relative orientations or positional relationships, which are only for the convenience of describing the present invention and simplifying the description. It is not indicated or implied that the indicated device or element must have a particular orientation, be constructed and operate in a particular orientation, and therefore should not be construed as limiting the invention. In addition, the terms "first", "second", etc. are used for descriptive purposes only, and should not be construed as indicating or implying relative importance or implying the number of indicated technical features. Thus, a feature defined as "first", "second", etc., may expressly or implicitly include one or more of that feature. In the description of the present invention, unless otherwise specified, "plurality" means two or more.
在本发明的描述中，需要说明的是，除非另有明确的规定和限定，术语“安装”、“相连”、“连接”应做广义理解，例如，可以是固定连接，也可以是可拆卸连接，或一体地连接；可以是机械连接，也可以是电连接；可以是直接相连，也可以通过中间媒介间接相连，可以是两个元件内部的连通。对于本领域的普通技术人员而言，可以通过具体情况理解上述术语在本发明中的具体含义。In the description of the present invention, it should be noted that the terms "installed", "connected" and "connected" should be understood in a broad sense, unless otherwise expressly specified and limited, for example, it may be a fixed connection or a detachable connection Connection, or integral connection; can be mechanical connection, can also be electrical connection; can be directly connected, can also be indirectly connected through an intermediate medium, can be internal communication between two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood through specific situations.
下面对本发明的具体实施例做详细说明。Specific embodiments of the present invention will be described in detail below.
如图1-图3所示，基于有限元分析的变厚度壳单元质心漂移量计算方法，包括以下步骤，As shown in Fig. 1-Fig. 3, the calculation method of centroid drift of variable thickness shell element based on finite element analysis includes the following steps:
S1、建立变厚度属性的壳截面，壳截面厚度为空间坐标的函数f(x,y,z,δ)＝0，对具有壳属性的几何模型分配变厚度截面属性，基于几何模型划分网格，设定边界条件，提交计算；S1. Establish a shell section with variable thickness attribute. The thickness of the shell section is a function of space coordinates f(x, y, z, δ) = 0, assign the variable thickness section attribute to the geometric model with the shell attribute, and divide the mesh based on the geometric model. , set the boundary conditions, and submit the calculation;
S2、建立二次开发程序，提取变形前网格节点，将四边形单元离散成三角形单元；S2. Establish a secondary development program, extract the mesh nodes before deformation, and discretize the quadrilateral elements into triangular elements;
S3、建立局部坐标系O'X'Y'Z'，取三角形长边为局部坐标系X'轴，长边的高所在的轴作为局部坐标系Y'轴，Z'轴按照右手定则确定；S3. Establish a local coordinate system O'X'Y'Z', take the long side of the triangle as the X' axis of the local coordinate system, the axis where the height of the long side is located as the Y' axis of the local coordinate system, and the Z' axis is determined according to the right-hand rule ;
S4、建立局部坐标系和整体坐标系的坐标转换矩阵M1，获取局部坐标系下壳截面厚度随空间坐标变化的函数g(x',y',z',δ)＝0；S4, establish the coordinate transformation matrix M1 of the local coordinate system and the global coordinate system, and obtain the function g(x', y', z', δ)=0 of the thickness of the shell section under the local coordinate system changing with the spatial coordinates;
S5、局部坐标系下对三角形单元进行积分，获得三角形单元的体积，结合材料密度获取三角形单元质量和局部坐标系下质心位置，根据坐标转换矩阵获得三角形单元在整体坐标系下质心位置，应用质心公式计算变形前结构整体质心；S5. Integrate the triangular element in the local coordinate system to obtain the volume of the triangular element, obtain the mass of the triangular element and the position of the centroid in the local coordinate system in combination with the material density, obtain the centroid position of the triangular element in the global coordinate system according to the coordinate transformation matrix, and apply the centroid The formula calculates the overall center of mass of the structure before deformation;
S6、按照步骤2的方法将变形后的四边形单元离散成三角形单元，按照步骤3的方法确定变形后三角形单元的局部坐标系O"X"Y"Z"；S6. Discrete the deformed quadrilateral unit into triangular units according to the method of step 2, and determine the local coordinate system O"X"Y"Z" of the deformed triangular unit according to the method of step 3;
S7、应用空间距离公式计算变形前后质心漂移量。S7. Calculate the displacement of the center of mass before and after the deformation by applying the spatial distance formula.
进一步的，在步骤S4中，坐标转换矩阵表述如下：Further, in step S4, the coordinate transformation matrix is expressed as follows:
将f(x,y,z,δ)＝0中的x、y、z参数通过坐标转换矩阵用x'、y'、z'代替，即得到局部坐标系下的壳厚度空间分布函数g(x',y',z',δ)＝0。Replace the x, y, z parameters in f(x, y, z, δ)=0 with x', y', z' through the coordinate transformation matrix, that is, the shell thickness spatial distribution function g( x', y', z', δ)=0.
进一步的，在步骤S5中，局部坐标系下体积和质心公式如下：Further, in step S5, the formulas of volume and centroid in the local coordinate system are as follows:
进一步的，在步骤S6中，单元特征尺寸不大于结构特征尺寸1/50时，单个三角形单元尺寸变形与该三角形单元整体位移相比为高阶小量，认为变形后局部坐标系下三角形单元质量和质心位置与变形前相同，以步骤S5确定的变形前三角形单元质心位置坐标作为变形后三角形单元在局部坐标系的质心坐标，以步骤S5确定的变形前三角形单元质量作为变形后三角形单元质量，根据变形后单元局部坐标系和整体坐标系的坐标转换矩阵M2，计算变形后三角形单元在整体坐标系下的质心位置，根据质心公式得到变形后结构整体质心位置。Further, in step S6, when the unit feature size is not greater than 1/50 of the structural feature size, the size deformation of a single triangular unit is a high-order small amount compared with the overall displacement of the triangular unit, and it is considered that the quality of the triangular unit in the local coordinate system after deformation is The position of the centroid is the same as that before the deformation, and the position coordinates of the centroid of the triangular element before the deformation determined in step S5 are taken as the centroid coordinates of the triangular element after the deformation in the local coordinate system, and the mass of the triangular element before the deformation determined in step S5 is taken as the mass of the triangular element after the deformation, According to the coordinate transformation matrix M2 of the local coordinate system and the global coordinate system of the deformed element, the centroid position of the deformed triangular element in the global coordinate system is calculated, and the overall centroid position of the deformed structure is obtained according to the centroid formula.
进一步的，坐标转换矩阵表述如下，Further, the coordinate transformation matrix is expressed as follows,
质心公式如下，The centroid formula is as follows,
其中ρ代表密度，x单元、y单元、z单元代表单元的质心坐标，V单元代表单元的体积， x质心、y质心、z质心代表结构整体质心坐标。Among them, ρ represents the density, the x, y, and z units represent the coordinates of the centroid of the unit , the V unit represents the volume of the unit , and the x, y , and z centroids represent the overall center of mass coordinates of the structure.
实施例：三轴气浮台中心承力筒为圆锥筒，圆锥筒模型见图2，加载方式为上端固定，Z向加载10g。Example: The central bearing cylinder of the triaxial air flotation platform is a conical cylinder. The model of the conical cylinder is shown in Figure 2. The loading method is to fix the upper end and load 10g in the Z direction.
首先对该计算方法的精度进行验证，由于abaqus有限元软件只能计算等厚度的壳单元质量属性，假定图2所示圆锥筒等壁厚，壁厚为10mm。使用abaqus有限元软件和本计算方法计算结果见表1，可以看出，两者质心漂移量误差小于2e-7mm。First, the accuracy of the calculation method is verified. Since the abaqus finite element software can only calculate the mass properties of shell elements with equal thickness, it is assumed that the conical cylinder shown in Figure 2 has the same wall thickness and the wall thickness is 10mm. The calculation results using abaqus finite element software and this calculation method are shown in Table 1. It can be seen that the error of the center of mass drift of the two is less than 2e-7mm.
表1 abaqus和本计算方法计算结果对比Table 1 Comparison of calculation results between abaqus and this calculation method
abaqus不能计算变厚度壳单元质心漂移量，使用本方法计算变厚度圆锥筒加载后质心漂移，圆锥筒截面见图3，加载方式为上端固定，Z向加载10g，计算结果见表2。Abaqus cannot calculate the centroid drift of the variable thickness shell element. This method is used to calculate the centroid drift of the variable thickness conical cylinder after loading. The section of the conical cylinder is shown in Figure 3.
表2变厚度圆锥筒模型加载后质心漂移Table 2 Drift of the center of mass after the variable thickness cone model is loaded
从计算结果可以看出，采用变厚度中心承力筒，承力筒横向刚度得到了加强，有利于气浮台干扰力矩的降低。It can be seen from the calculation results that the use of the variable-thickness central bearing tube increases the lateral stiffness of the bearing tube, which is beneficial to the reduction of the disturbance moment of the air-floating table.
以上对本发明的一个实施例进行了详细说明，但所述内容仅为本发明的较佳实施例，不能被认为用于限定本发明的实施范围。凡依本发明申请范围所作的均等变化与改进等，均应仍归属于本发明的专利涵盖范围之内。An embodiment of the present invention has been described in detail above, but the content is only a preferred embodiment of the present invention, and cannot be considered to limit the scope of the present invention. All equivalent changes and improvements made according to the scope of the application of the present invention should still belong to the scope of the patent of the present invention.
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