矩形薄板在垂直均布压力作用下变形与模态分析
本文基于ANSYS 10.0平台上，对钢架结构的矩形薄板变形、立柱所受弯矩及整体钢架结构的模态进行了分析。文中分析时，根据其具体结构对矩形薄板采用了板壳模型，立柱采用了空间梁模型，合理的简化了ANSYS对此钢架结构的分析，从而缩短了计算时间，提高了工作效率。1、引 言薄板和立柱组合的钢架结构在日常生活中应用非常广泛，例如凳子、桌子、简易房屋等，因此对其进行力学分析有着十分重要的意义。顶部薄板在垂直方向的尺寸远小于其他两个方向的尺寸，且只受到垂直于薄板方向的力，因此可将其简化为板桥问题进行求解；其支撑立柱受到包括弯矩在内的全约束，而杆单元适用于只受轴向力方向的情形，因此采用梁单元较为合理。在对钢架结构如此简化后再分析矩形薄板变形、立柱所受弯矩及钢架结构模态时，不仅合理可行，而且提高了计算效率。2、计算模型问题描述：如图所示钢架结构，材料的参数为弹性模量，密度，泊松比，它在台面上受到顶部的均布载荷作用。求所示顶盖的位移，立柱的弯矩及所示结构的前五阶固有频率与振型。问题详细说明：ANSYS有限元分析过程主要包括三个步骤：1.创建有限元模型—前处理1）单元类型：矩形薄板 Shell63；立柱Beam4。2）实常数：矩形薄板 板厚。立柱 横截面面积；z轴惯性矩；y轴惯性矩； z轴方向厚度；y轴方向厚度3）定义材料属性：弹性模量；泊松比；密度4）构建几何模型并进行网格划分。2.施加载荷并求解1）施加约束与载荷。2）对有限元模型进行静态求解。3）对有限元模型进行静态求解。3.查看分析结果，检验结果的正确性。A静态分析1）顶盖的位移图，如图2所示2）立柱的弯矩图，如图3所示B模态分析1）模态分析的前五阶固有频率如下表模态分析的前五阶固有频率表2）模态分析的前五阶固有频率振型来源：CAE技术联盟
3、结 论本文在对此钢架结构进行有限元分析时， 把顶盖看作是板壳单元，把立柱看作梁单元，简化了对钢架结构分析模型。通过实际的计算与分析，说明这种简化是可行的，能够解决此类结构的变形、强度和振动问题。log文件（命令流方式）：/BATCH ! /COM,ANSYS RELEASE 10.0 UP20050718 20:39:08 12/08/2012 ! /REPLOT,RESIZE !* /NOPR/PMETH,OFF,0KEYW,PR_SET,1KEYW,PR_STRUC,1KEYW,PR_THERM,0KEYW,PR_FLUID,0KEYW,PR_ELMAG,0KEYW,MAGNOD,0KEYW,MAGEDG,0KEYW,MAGHFE,0KEYW,MAGELC,0KEYW,PR_MULTI,0KEYW,PR_CFD,0/GO!* ! /COM,! /COM,Preferences for GUI filtering have been set to display:! /COM,Structural!* /PREP7 !* ET,1,SHELL63!* ET,2,BEAM4 !* R,1,0.01, , , , , ,RMORE, , , ,RMORERMORE, ,!* R,2,1.6e-3,2.1333333333e-6,2.1333333333e-6,0.04,0.04, ,RMORE, , , , , , , !* !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDATA,EX,1,,2.1e11MPDATA,PRXY,1,,0.3 K,1,0.45,-0.75,0,K,2,0.45,0.75,0,K,3,-0.45,0.75,0,K,4,-0.45,-0.75,0, K,8,-0.45,-0.75,1, K,7,-0.45,0.75,1,K,6,0.45,0.75,1,K,5,0.45,-0.75,1,FLST,2,4,3 FITEM,2,5FITEM,2,6FITEM,2,7FITEM,2,8A,P51X LSTR, 1, 5 LSTR, 2, 6 LSTR, 3, 7 LSTR, 4, 8 ! /PNUM,KP,1 ! /PNUM,LINE,1! /PNUM,AREA,1! /PNUM,VOLU,0! /PNUM,NODE,0! /PNUM,TABN,0! /PNUM,SVAL,0! /NUMBER,0!* ! /PNUM,ELEM,0! /REPLOT!* ! LPLOT! /ANG,1,90,XS,1 ! /REP,FAST! /ANG,1,-90,XS,1! /REP,FAST! /ANG,1,-90,XS,1! /REP,FAST! /ANG,1,-90,ZS,1! /REP,FAST! /ANG,1,90,ZS,1 ! /REP,FAST! /ANG,1,90,ZS,1 ! /REP,FAST! /ANG,1,-90,ZS,1! /REP,FAST! /USER,1! /VIEW,1,0.998255801462 ,0.589153299942E-01,0.378665282075E-02! /ANG, 1,-92.7751372861 ! /REPLO ! /VIEW,1,0.979366750107 ,0.641923117955E-01,0.191624935462! /ANG, 1,-93.5302849705 ! /REPLO ! /DIST,1,0.788943034604,1! /REP,FAST! /DIST,1,1.26751863714,1! /REP,FAST! /DIST,1,1.26751863714,1! /REP,FAST! /VIEW,1,0.982195407775 ,0.651495933705E-01,0.176203607878! /ANG, 1,-93.4720666726 ! /REPLO
来源：CAE技术联盟
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来源：技术联盟
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