1、有限元的分析与编程应用求解报告一、 问题的描述如图所示三角形截面简支梁，底边中点受载荷 P 作用，已知P=L=E=1， =0，厚度 h=1.按平面应力考虑。用尽可能简单的有限元法计算载荷作用点位移。二、 问题的分析按平面应力考虑，作用于三角形简支梁上的载荷平行于截面且沿纵向方向分布。选择单元类型为：三结点常应变单元。三、 问题的求解已知弹性模量 E=1，泊松比 u=0，厚度 h=1。结点的选择如图所示：运算后得出如下结果：Y 轴方向上的应力分布图：如上所示模型中，点 1 和点 2 为固定节点，在 L1 中间位置的节点 4 上施加p=-1 的载荷。其网格分布如下图：由图可得：单元类型 最小位移(
2、mm）最大位移(mm) 最小应力(Pa) 最大应力(Pa)常应变三结点单元0 15.562 -13.983 10.891本题要求载荷作用点位移，即最大位移为：15.562其位移分布图：四、 ANSYS 程序代码：/COM, Structural !* /PREP7 !* ET,1,BEAM3 !* !* ETDEL,1 !* ET,1,PLANE42!* !* MPTEMP, MPTEMP,1,0 MPDATA,EX,1,1 MPDATA,PRXY,1,0K,1,0,0,0, K,2,2,0,0, K,3,1,1,0, LSTR, 1, 2 LSTR, 2, 3 LSTR, 3, 1 !* H
3、PTCREATE,LINE,1,0,COORD,1,0,0, CM,_Y,LINE LSEL, , , , 1 CM,_Y1,LINE CMSEL,S,_Y !* !* CMSEL,S,_Y1 LATT,1, ,1, , , , CMSEL,S,_Y CMDELE,_Y CMDELE,_Y1 !* CM,_Y,LINE LSEL, , , , 1 CM,_Y1,LINE CMSEL,S,_Y !* !* CMSEL,S,_Y1 LATT,1, ,1, , , , CMSEL,S,_Y CMDELE,_Y CMDELE,_Y1 !* CM,_Y,LINE LSEL, , , , 1 CM,_Y1
4、,LINE CMSEL,S,_Y !* FLST,5,1,4,ORDE,1 FITEM,5,1 CM,_Y,LINE LSEL, , , ,P51X CM,_Y1,LINE CMSEL,_Y !* LESIZE,_Y1, , ,20, , , , ,1 !* FLST,5,1,4,ORDE,1 FITEM,5,3 CM,_Y,LINE LSEL, , , ,P51X CM,_Y1,LINE CMSEL,_Y !* LESIZE,_Y1, , ,20, , , , ,1 !* FLST,5,1,4,ORDE,1 FITEM,5,2 CM,_Y,LINE LSEL, , , ,P51X CM,_Y
5、1,LINE CMSEL,_Y !* LESIZE,_Y1, , ,20, , , , ,1 !* FLST,2,3,4,ORDE,2 FITEM,2,1 FITEM,2,-3 LMESH,P51X MSHAPE,0,2D MSHKEY,0!* FLST,2,3,4,ORDE,2 FITEM,2,1 FITEM,2,-3 LMESH,P51X FLST,2,3,4 FITEM,2,3 FITEM,2,2 FITEM,2,1 AL,P51X CM,_Y,AREA ASEL, , , , 1 CM,_Y1,AREA CHKMSH,AREA CMSEL,S,_Y !* AMESH,_Y1 !* CM
6、DELE,_Y CMDELE,_Y1 CMDELE,_Y2 !* FINISH /SOLFINISH /PREP7 FINISH /SOLFLST,2,1,3,ORDE,1 FITEM,2,4 FLST,2,2,3,ORDE,2 FITEM,2,1 FITEM,2,-2 !* /GO DK,P51X, ,0, ,0,UX,UY, , , , , FLST,2,1,3,ORDE,1 FITEM,2,4 !* /GO FK,P51X,FY,-1 /STATUS,SOLUSOLVE FINISH /POST1 !* /EFACET,1 PLNSOL, S,XY, 0,1.0 !* PLESOL, S,XY, 0,1.0
