LSDyna在土木工程静力问题中的应用
2024-05-11 07:50:11
一. 梁单元
1. 理论
简支梁，受向下的均布力作用q=1kN/m, 梁的跨度l=10m，E=2×10^5kPa，μ=0.2，梁的截面参数宽度B，高度H
跨中挠度的理论解是y=5ql^4/384EI
(1)B=0.5m，H=0.5m，y=0.125
(2)B=1.0m，H=0.5m，y=0.0625
2. 模型
(1)
*KEYWORD
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ NODE DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*NODE
$ nid n1 n2 n31 0 0 02 1 0 03 2 0 04 3 0 05 4 0 06 5 0 07 6 0 08 7 0 09 8 0 010 9 0 011 10 0 012 5 1 0
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ ELEMENT DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*ELEMENT_BEAM
$ eid mid n1 n2 n31 1 1 2 122 1 2 3 123 1 3 4 124 1 4 5 125 1 5 6 126 1 6 7 127 1 7 8 128 1 8 9 129 1 9 10 1210 1 10 11 12
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ BOUNDARY DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*BOUNDARY_SPC_NODE
$# nsid cid dofx dofy dofz dofrx dofry dofrz1 0 1 1 0 0 0 011 0 0 1 0 0 0 0
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ PARTS DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*PART
beam
$ pid secid mid1 1 1
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ MATERIAL DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*MAT_ELASTIC
$ mid ro e pr da db1 200 2e5 0.2
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ SECTION DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*SECTION_BEAM
$ sid elform shrf qr/irid cst 1 2
$ a iss itt j sa 0.25 0.005208 0.005208 0
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ LOAD DEFINITIONS $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*SET_BEAM
$ sid1
$ k1 k2 k3 k4 k5 k6 k7 k81 2 3 4 5 6 7 89 10
*LOAD_BEAM_SET
$ esid dal lcid sf1 2 1
*DEFINE_CURVE
$ lcid1
$ abscissa ordinate0.0 1200 1
*DAMPING_GLOBAL
$ lcid VALDMP1 10
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ Control output $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*CONTROL_TERMINATION200
*CONTROL_TIMESTEP0.0000 0.9000 0 0.00 0.00
*END
y=0.1244
(2)
*KEYWORD
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ NODE DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*NODE
$ nid n1 n2 n31 0 0 02 1 0 03 2 0 04 3 0 05 4 0 06 5 0 07 6 0 08 7 0 09 8 0 010 9 0 011 10 0 012 5 1 0
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ ELEMENT DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*ELEMENT_BEAM
$ eid mid n1 n2 n31 1 1 2 122 1 2 3 123 1 3 4 124 1 4 5 125 1 5 6 126 1 6 7 127 1 7 8 128 1 8 9 129 1 9 10 1210 1 10 11 12
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ BOUNDARY DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*BOUNDARY_SPC_NODE
$# nsid cid dofx dofy dofz dofrx dofry dofrz1 0 1 1 0 0 0 011 0 0 1 0 0 0 0
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ PARTS DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*PART
beam
$ pid secid mid1 1 1
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ MATERIAL DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*MAT_ELASTIC
$ mid ro e pr da db1 200 2e5 0.2
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ SECTION DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*SECTION_BEAM
$ secid elform shrf qr1
$ ts1 ts2 tt1 tt20.5 0.5 1.0 1.0
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ LOAD DEFINITIONS $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*SET_BEAM
$ sid1
$ k1 k2 k3 k4 k5 k6 k7 k81 2 3 4 5 6 7 89 10
*LOAD_BEAM_SET
$ esid dal lcid sf1 2 1
*DEFINE_CURVE
$ lcid1
$ abscissa ordinate0.0 1200 1
*DAMPING_GLOBAL
$ lcid VALDMP1 10
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ Control output $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*CONTROL_TERMINATION200
*CONTROL_TIMESTEP0.0000 0.9000 0 0.00 0.00
*END
y=0.06173
3. 说明
计算静力问题，需设置*DAMPING_GLOBAL，且分析时间足够长，使结构稳定。
二. 线性弹簧
1. 理论
一线性弹簧，一端固定，弹簧长10m，弹簧刚度为K=100N/m
(1)一端受轴向力F=100N，自由端理论解为s=F/k=1m
(2)一端受轴向位移s=1m，弹簧受力理论解为F=s*k=100N
(3)一端受切向位移s=1m，弹簧受力理论解为F=4.99N
2. 模型
(1)
*KEYWORD
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ NODE DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*NODE1 0 0 02 10 0 0
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ ELEMENT DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*ELEMENT_DISCRETE
$ eid pid n1 n21 1 1 2
*ELEMENT_MASS
$ eid id mass2 1 0.001
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ BOUNDARY DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*BOUNDARY_SPC_NODE
$# nsid cid dofx dofy dofz dofrx dofry dofrz2 0 1 1 1 1 1 1
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ PARTS DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*SECTION_DISCRETE
$ secid dro1 0 0 0 0 00 0
*MAT_SPRING_ELASTIC
$ mid k1 100
*PART
spring
$ pid secid mid1 1 1
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ LOAD DEFINITIONS $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*LOAD_NODE_POINT
$ nid dof lcid1 1 1
*DEFINE_CURVE10.0 100200 100
*DAMPING_GLOBAL
$ lcid VALDMP0 100
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ Control output $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*CONTROL_TERMINATION200
*CONTROL_TIMESTEP0.0000 0.9000 0 0.00 0.00
*END
s=1.00
(2)
*KEYWORD
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ NODE DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*NODE1 0 0 02 10 0 0
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ ELEMENT DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*ELEMENT_DISCRETE
$ eid pid n1 n21 1 1 2
*ELEMENT_MASS
$ eid id mass2 1 0.001
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ BOUNDARY DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*BOUNDARY_SPC_NODE
$# nsid cid dofx dofy dofz dofrx dofry dofrz2 0 1 1 1 1 1 1
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ PARTS DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*SECTION_DISCRETE
$ secid dro1 0 0 0 0 00 0
*MAT_SPRING_ELASTIC
$ mid k1 100
*PART
spring
$ pid secid mid1 1 1
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ LOAD DEFINITIONS $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*BOUNDARY_PRESCRIBED_MOTION_NODE
$ NODE DOF VAD LCID SF1 1 2 1 1
*DEFINE_CURVE10.0 0.0200 1.0
*DAMPING_GLOBAL
$ lcid VALDMP0 100
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ Control output $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*CONTROL_TERMINATION200
*CONTROL_TIMESTEP0.0000 0.9000 0 0.00 0.00
*END
F=100.1
(3)
*KEYWORD
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ NODE DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*NODE1 0 0 02 10 0 0
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ ELEMENT DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*ELEMENT_DISCRETE
$ eid pid n1 n21 1 1 2
*ELEMENT_MASS
$ eid id mass2 1 0.001
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ BOUNDARY DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*BOUNDARY_SPC_NODE
$# nsid cid dofx dofy dofz dofrx dofry dofrz1 0 1 0 1 1 1 12 0 1 1 1 1 1 1
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ PARTS DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*SECTION_DISCRETE
$ secid dro1 0 0 0 0 00 0
*MAT_SPRING_ELASTIC
$ mid k1 100
*PART
spring
$ pid secid mid1 1 1
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ LOAD DEFINITIONS $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*BOUNDARY_PRESCRIBED_MOTION_NODE
$ NODE DOF VAD LCID SF1 2 2 1 1
*DEFINE_CURVE10.0 0.0200 1.0
*DAMPING_GLOBAL
$ lcid VALDMP0 100
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ Control output $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*CONTROL_TERMINATION200
*CONTROL_TIMESTEP0.0000 0.9000 0 0.00 0.00
*END
F=4.964
3. 说明
弹簧需连接到有质量的单元，单独设置一个有质量的点用*ELEMENT_MASS
三. 非线性弹簧
1. 理论
将“二、线性弹簧”中的弹簧刚度设为如下所示
(1)当弹簧受轴向力F=100N，自由端位移s=4m
2. 模型
(1)
*KEYWORD
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ NODE DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*NODE1 0 0 02 10 0 0
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ ELEMENT DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*ELEMENT_DISCRETE
$ eid pid n1 n21 1 1 2
*ELEMENT_MASS
$ eid id mass2 1 0.001
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ BOUNDARY DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*BOUNDARY_SPC_NODE
$# nsid cid dofx dofy dofz dofrx dofry dofrz2 0 1 1 1 1 1 1
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ PARTS DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*SECTION_DISCRETE
$ secid dro1 0 0 0 0 00 0
*MAT_SPRING_NONLINEAR_ELASTIC
$ MID LCD1 2
*DEFINE_CURVE2
$ DISPLACEMENT FORCE-2.5 -50-1.0 -0.010 01.0 0.012.5 100
*PART
spring
$ pid secid mid1 1 1
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ LOAD DEFINITIONS $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*LOAD_NODE_POINT
$ nid dof lcid1 1 1
*DEFINE_CURVE10.0 0100 100200 100
*DAMPING_GLOBAL
$ lcid VALDMP0 100
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ Control output $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*CONTROL_TERMINATION200
*CONTROL_TIMESTEP0.0000 0.9000 0 0.00 0.00
*END
s=4.00
3. 说明
- 非线性弹簧，位移-力曲线，即使有位移，没有力，也不能设置为0，如本例子，在横坐标1处纵坐标只能设一个很小的值，如0.1。
- 对于有弹簧结构，荷载不要一下全部加上，瞬间会导致变形非常大。
四. 壳单元
1. 理论
正方形薄板边长L=2m，厚度h=0.01m，四边固支。薄板弹性模量E=200GPa，泊松比u-0.3。板中心受垂直集中载荷Q=400N作用，板的中心挠度理论解为w=0.0056QL^2/D，其中D=Eh^3/12(1-u^2)，代入求解得w=0.000489216
2. 模型
*KEYWORD
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ NODE DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*NODE1 0 0 02 0.5 0 03 1 0 04 1.5 0 05 2 0 06 0 0.5 07 0.5 0.5 08 1 0.5 09 1.5 0.5 010 2 0.5 011 0 1 012 0.5 1 013 1 1 014 1.5 1 015 2 1 016 0 1.5 017 0.5 1.5 018 1 1.5 019 1.5 1.5 020 2 1.5 021 0 2 022 0.5 2 023 1 2 024 1.5 2 025 2 2 0
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ ELEMENT DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*ELEMENT_SHELL1 1 1 2 7 62 1 2 3 8 73 1 3 4 9 84 1 4 5 10 95 1 6 7 12 116 1 7 8 13 127 1 8 9 14 138 1 9 10 15 149 1 11 12 17 1610 1 12 13 18 1711 1 13 14 19 1812 1 14 15 20 1913 1 16 17 22 2114 1 17 18 23 2215 1 18 19 24 2316 1 19 20 25 24
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ BOUNDARY DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*SET_NODE_LIST_TITLE
Fixed all11 2 3 4 5 6 10 1115 16 20 21 22 23 24 25
*BOUNDARY_SPC_SET
$# nsid cid dofx dofy dofz dofrx dofry dofrz1 0 1 1 1 1 1 1
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ PARTS DEFINITION $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*SECTION_SHELL10.01 0.01 0.01 0.01 0
*MAT_ELASTIC
$ mid ro e pr1 200 2.0e11 0.3
*PART
spring
$ pid secid mid1 1 1
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ LOAD DEFINITIONS $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*LOAD_NODE_POINT
$ nid dof lcid13 3 1
*DEFINE_CURVE10.0 400200 400
*DAMPING_GLOBAL
$ lcid VALDMP0 100
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ Control output $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
*CONTROL_TERMINATION200
*CONTROL_TIMESTEP0.0000 0.9000 0 0.00 0.00
*END
w=0.0004551
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