基于LS-DYNA隐式分析计算网壳结构振动模态
本文以一个球面网壳结构为例，介绍基于LS-DYNA的隐式分析实现结构模态计算的过程。
球面网壳结构球面半径为20.0m，跨度约35m，矢跨比1：3.5，如图1所示。结构所有杆件均采用Φ114.0×4.0的Q235圆形钢管。球面网壳结构的质量应按重力荷载代表值计算，除了结构自重由程序自动计算外，还需要包括其他永久荷载及可变荷载组合值，本例中这部分质量按水平投影面积100kg/m2计算，平均分配到网壳的全部内部节点（共计91个），每个内部节点大约分配附加质量1000kg。约束情况为约束底部周边节点的线位移自由度。
图1 球面网壳的俯视图
可以在Mechanical APDL中采用直接法创建有限元模型，涉及到的单元类型包括BEAM161以及MASS166，具体建模过程从略，建模完成后写出K文件。创建完成后的模型及约束情况如图2所示。
图2 球面网壳计算模型及周边支撑情况
打开关键字文件，在其中添加隐式分析与特征值分析相关的如下关键字：
*CONTROL_TERMINATION
*CONTROL_IMPLICIT_GENERAL
*CONTROL_IMPLICIT_EIGENVALUE
关键字文件修改完成后，递交LS-DYNA求解器进行计算。完成求解后打开计算输出的eigout文件，特征值计算结果（CYCLES列为频率）如图3所示。
图3 特征值计算结果
打开LS-Prepost，按下Ctrl+B快捷键，指向计算路径下的d3eigv文件并打开，按“+”号即可观察各阶振型，每一节振型可通过向前动画播放按钮动画显示和观察。各阶振型的前视图如图4、图5所示。
图4网壳结构振型
图5网壳结构振型（后三阶）
附：本文关键字文件Modal_DYNA.k（单元、节点信息有删减）
*KEYWORD
*TITLE
$
*DATABASE_FORMAT
0
$
$
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ NODE DEFINITIONS $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$
*NODE
1 1.732050808E+04 0.000000000E+00 1.000000000E+04 0 0
2 1.627595363E+04 5.923962655E+03 1.000000000E+04 0 0
3 1.326827896E+04 1.113340798E+04 1.000000000E+04 0 0
......
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ SECTION DEFINITIONS $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$
*SECTION_BEAM
1 5 1.0000 2.0 1.0
114. 114. 106. 106. 0.00 0.00
$
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ MATERIAL DEFINITIONS $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*MAT_ELASTIC
1 0.785E-08 0.206E+06 0.300000 0.0 0.0 0.0
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ PARTS DEFINITIONS $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*PART
Part 1 for Mat 1 and Elem Type 1
1 1 1 0 0 0 0
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ ELEMENT DEFINITIONS $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*ELEMENT_BEAM
1 1 1 2 200
2 1 2 3 200
3 1 3 4 200
......
*ELEMENT_MASS
307 19 1.000000000E+00
308 20 1.000000000E+00
309 21 1.000000000E+00
......
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ BOUNDARY DEFINITIONS $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$
*SET_NODE_LIST
1 0.000 0.000 0.000 0.000
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16
17 18
*BOUNDARY_SPC_SET
1 0 1 1 1 0 0 0
$
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ CONTROL OPTIONS $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$
*CONTROL_TERMINATION
0.500E-01 0 0.00000 0.00000 0.00000
*CONTROL_IMPLICIT_GENERAL
1,0.05,2,,2,
*CONTROL_IMPLICIT_EIGENVALUE
6
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ TIME HISTORY $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$
*DATABASE_BINARY_D3PLOT
0.5000E-03
*DATABASE_BINARY_D3THDT
0.5000E-04
$
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ DATABASE OPTIONS $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$
*DATABASE_EXTENT_BINARY
0 0 3 1 0 0 0 0
0 0 4 0 0 0
*END
