Shell Elements
Shell Elements (/PROP/SHELL)
A shell is defined by a curved midsurface and a thickness h, which is supposed to be very small compared to the two other dimensions. A shell element is the most common element; a full car crash model is made of at least 90% shell elements.
Even if the Kirchhoff model is less accurate, if the ratio L/h is greater than 20, the statements made by Kirchhoff are correct; but if the ratio L/h is between 10 and 20, the assumption stating that a plane orthogonal to the midplane remains orthogonal during the deformation is no longer valid, and the Mindlin plate model must be considered in which transverse shear strain is taken into account. In Radioss, underintegrated shell elements (both 4node and 3node shell) are based on Mindlin assumptions. There is no specific formulation that enables to offset the midplane of the element away from the nodes; therefore, it is very important to discretize structures with thin walls on the midsurface.
Mesh  Element Name  Number of Integration Points  Hourglass Formulation  Comments 

BT
(Classic Q4) 
1  Four types based on penalty method  Constant normal
vector Hourglass formulations types 3 and 4 are much better than type 1  used by default 

QEPH  1  Physical stabilization  Normal vectors at
nodes No hourglass energy in output 

QBAT  2x2  Fullyintegrated element  Normal vectors at
nodes No hourglass energy 

C0  1    Flat facet
element No hourglass energy 

DKT18  3    Kirchhoff shell
(thin shell only) Higher t/L, lower the time step 

S3N6  1    Kirchhoff shell
(thin shell only) No rotational DOF Rotation of the sides is determined with the help of vertical displacements in neighbors 
 The BT element is simple, efficient and has a low cost. As it is underintegrated, the element is not very sensitive to the mesh quality and can be used for the case of coarse mesh.
 For cases of QuasiStatic Analysis, fine mesh, warped surface and buckling, it is advisable to use QEPH or QBAT elements.
 QBAT is the most accurate element in Radioss. However, as it is fullyintegrated, it costs two to three times more than a BT element.
 QEPH is the best compromise between cost and quality. Generally, it costs no more than 15% of a BT element and the results obtained by this element are close to those of QBAT.
 Triangles are not recommended. A C0 element is too stiff and DKT18 comes with a high cost. The number of total triangles in a mesh is generally limited to 5% to ensure a good quality.
 The S3N6 element has as good a behavior in bending as DKT18. It can also be used for some special applications, such as stamping simulations.
Integration through Thickness
In an elastic shell, the normal stress variation through the thickness is linear; therefore, the internal energy can be obtained by analytical integration. In case of plasticity, the stress distribution becomes nonlinear and a minimum of three integration points are required to take the nonlinearity into account. The nonlinear distribution of stress can be approached by measuring values at some added integration points. The quality of internal energy estimation depends on the number of integration points and the cost. A good compromise between cost and quality can be found, taking into account, material nonlinearity, thickness and bending rate. The number of integration points can be increased up to 10 in Radioss V5x. Using five integration points will provide better results; especially if the thickness is greater than 2mm, but the increase in CPU time is not negligible. To emulate a membrane element with no bending or transverse shear, it is enough to use only one integration point. For an elastic material (LAW1) due to the analytical computation, the option is ignored.
One way to get accurate results with a low CPU cost is to use the global integration. It consists in the transformation of von Mises plasticity criteria, in a socalled Iluyshin criteria, where the stress components at integration points are replaced by internal forces (N, M, T, etc.).
Iterative Plastic Projection
In plasticity computation, two fundamental assumptions must be satisfied. First, the stress in the plastic region must verify the plasticity criteria (for example, von Mises criteria). Second, in the principal stresses space is the direction ($\text{\Delta}\sigma $), due to work hardening is normal to the yield surface.
Thickness Variation
By default, shell thickness is supposed constant during shell deformation. Initial thickness is used to compute strains and to integrate stresses, but the thickness variation is still computed for postprocessing reasons. If a variable thickness (I_{thick} =1) is used, true thickness is computed not only for postprocessing, but also for strain computation and stresses integration.
Element Option Guidelines
Applications  Material  Property  Hourglass  Number of Integration Points  Thickness  Plasticity 

Basic crash  2  1  1  0 (global)  Constant  Radial 
Crash with trapezoidal wrapped shells and with global rotation  2  1  3(c) or QEPH  0 (global)  Constant  Radial 
Crash with spring back medium accuracy  2/36  1  1  3  Constant  Iteration 
Crash with spring back high accuracy  2/36  1  3(c) or QEPH  3  Variable  Iteration 
Crash with material failure ductile failure  2/36 (a)  1  1  5  Variable  Iteration 
High quality crash  2/36 (a)  1  3(c) or QEPH  5  Variable  Iteration 
Crash with material failure brittle failure  27  11  1  3/5  Variable  Iteration 
Windshield  27  11  1  3+1+3(b)  Variable  Iteration 
Membrane or Fabric  1/2/19/36  1  1  1  cst/var  rad/iter 
Composite  25  9/10/11  1  1 to 30  not used  not used 
Model with local hourglass excitation  2/...  1  3(c) or QEPH  0/3/5  
Model with low plasticity and low velocities  2/...  1  3(c) or QEPH  3/5 
 With variable thickness and iterative plasticity it is possible to model necking failure. The material hardening must be accurate.
 For glass, plastic, and glass windshield (3 glass layers, 1 plastic layer and 3 glass layers). Less accuracy, 2+1+2 can also be used. For more complex glass plastic windshields, more layers can be used.
 If elastoplastic hourglass (3) is used, it is recommended to use 0.1 for hm and hf and default for hr.