Description of Sample Problems
This document is an introduction to some of the features of LS-DYNA. New features are being constantly developed and added to LS-DYNA, and many of the newer capabilities are not described in this document. If the following problems are taken as a starting point, the incorporation of improved shell elements, different material models, and other new features can be approached in a step-by-step procedure with a high degree of confidence.
The following ten sample problems are given for your introduction to LS-DYNA: Sample 1: Bar Impacting a Rigid Wall
Sample 2: Impact of a Cylinder into a Rail
Sample 3: Impact of Two Elastic Solids
Sample 4: Square Plate Impacted by a Rod
Sample 5: Box Beam Buckling
Sample 6: Space Frame Impact
Sample 7: Thin Beam Subjected to an Impact
Sample 8: Impact on a Cylindrical Shell
Sample 9: Simply Supported Flat Plate
Sample 10: Hourglassing of Simply Supported Plate
Once completing a review of this document, it is highly recommended that you proceed to the LS-DYNA3D Keyword Manual as the next step for additional understanding of the features of LS-DYNA.
全面从严治党永远在路上Sample 1: Bar Impacting a Rigid Wall
Sample 1 simulates a cylindrical bar (3.24 centimeters in length) with a radius of 0.32 centimeters impacting a rigid wall at a right angle (normal impact). The finite element model has three planes of symmetry. The first two planes correspond to the x-z and y-z surfaces (e Figure 1 for finite element mesh). The two symmetry planes yield a quarter ction model which reduces the number of elements by a factor of four over a full model with no loss in accuracy. Eight-node continuum brick elements are ud.
Figure 1. Sample 1 mesh.毛笔字大全
The third symmetry plane corresponds to the front x-y surface of the mesh, and simulates a rigid wall. This could have been modeled using either a rigid wall or sliding surface definitions at greater
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CPU cost.
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A bilinear elastic/plastic material model (model 3) was ud with the properties of copper. Isotropic strain hardening is included. The material properties ud are summarized in Table 1.
The bar is given an initial velocity of 2.27x10-2 centimeters/microconds in the negative z-direction. View the time quence of the deforming mesh. Also, view the contour deformation time quence in the z-direction. The displacement respon shows a total z-displacement of -1.087 centimeters. Thus the final length of the 3.24 centimeters long bar is 2.15 centimeters.
Material Model3
Density (g/cm3)8.93
Elastic Modulus (g/µc2 cm) 1.17
Tangent Modulus (g/µc2 cm) 1.0x10-3
Yield Strength (g/µc2 cm) 4.0x10-3
Poisson’s Ratio0.33
Hardening Parameter 1.0钢甲铁拳
Table 1. Material properties.
View the time quence of the deforming mesh with contours of effective plastic strain. Note that the boundary of plastic deformation moves up the bar in time. Also note the extreme plastic strain near the impact surface. The model predicts a maximum plastic strain of almost 300% in this localized region.
Sample 2: Impact of a Cylinder into a Rail
Sample 2 models a hollow circular cylinder impacting a rigid rail in the radial direction. The cylinder is 9 inches in diameter by 12 inches long with a 1/4 inch wall thickness. A rigid ring is added to each end to increa stiffness and mass. The cylinder is given an initial velocity of 660 inches/cond toward the rail.投诉信英语作文模板
One quarter of the cylinder was modeled using two planes of symmetry. Figure 2 shows the finite element mesh. The first plane of symmetry is the x-y plane on the right side of the mesh. The cond plane of symmetry is the y-z plane. The rail is modeled using a stonewall plane on the top s
urface. The other surfaces of the rail are added for graphic display clarity and rve no other purpo. Approximately 70 nodes on the cylinder in the vicinity of the rail are slaved to the stonewall.
Figure 2. Sample 2 mesh.
The cylinder model has three brick elements through the wall thickness. This is the minimum number required to capture bending stress with plasticity. Note the higher element density in the vicinity of the rail. The modeler anticipated that this region would undergo the most deformation and decread element density away from the rail to minimize the cost of the analysis.
The cylinder us an isotropic elastic/plastic material model (model 12) with the elastic perfectly plastic material properties of steel. The rigid support ring on the end of the cylinder us material model 1, to reprent a perfectly elastic material with twice the stiffness of steel. The density of this material is approximately 20 times that of steel. Table 2 gives a summary of the material properties.
Steel cylinder Added mass
Material Model121
Density (lb-c2/in4)7.346x10-4 1.473x10-2
Shear Modulus (lb/in2) 1.133x105N/A
Yield Strength (lb/in2) 1.90x105N/A
Hardening Modulus (lb/in2)0.0N/A
阅读日记Bulk Modulus (lb/in2) 2.4x107N/A
Elastic Modulus (lb/in2)N/A60x106
Table 2. Material properties.
美白全身View the time quence of the deforming mesh. View the time history of the rigid body displacement (node 4987) of the support ring in the y-direction. A maximum displacement of -1.77 inches occurs at 4.6 milliconds, after which the structure los its elastic strain energy and rebounds upward.
View the time history of the difference in nodal displacements (y-direction) between nodes 205 and 860. Node 205 is located on the outside surface of the cylinder near the center of the rail. Node 860 is located on the outside of the cylinder near the lower end of the support ring. The difference between the y-displacements of the nodes is a measure of the depth of the dent in the cylinder. It is en that there is a maximum relative displacement of 1.70 inches which then stabilizes to a 1.51 inch dent after the elastic strain energy is recovered. Experimental measurements recorded a maximum residual dent of 1.44 inches. The post-peak oscillations are due to elastic vibration of the cylinder about its deformed shape.
View the contours of effective plastic strain after the impact (t = 6.4 milliconds). Most of the contours shown reprent less than 17% plastic strain. Some very localized plastic strain of up to 29% is predicted on the outer surface at the center of the rail.
