5. Validation

To judge the relevance of the thick shell formulation, the following few application examples concern both linear statics and the calculation of natural modes. Three new test cases relating to the two finite elements described in the previous parts have been integrated in*Code_Aster*. They enrich the test cases of plate elements already present in the Code_Aster environment. A large part of these test cases have been listed in [bib10].

The three new test cases, two static plus one dynamic, are classic validation examples taken from [bib3]. The reference solutions, analytical or numerical, from [bib3] are compared to the numerical results given by*Code_Aster*. For more information on these test cases, refer to the validation documentation provided in reference.

5.1. Test case in linear statics

5.1.1. Static test case no. 1

The first test case is that of a cylindrical panel subjected to its own weight [V3.03.107].

This test makes it possible to demonstrate membrane effects that are greater than those of flexure. It makes it possible to measure the performance of shell elements compared to elements DKT or DKQ whose membrane interpolation is linear.

5.1.2. Static test case no. 2

The second test case is that of a helical shell subjected to two types of concentrated loading [V3.03.108].

The helical shape of the shell makes it possible to study the geometric representation of finite elements. Concentrated loads can be:

• in the plane: the influence due to membrane effects is then not important and the dominant behavior is that due to flexure,

• out of plane: membrane effects affect the behavior of the shell.

5.2. Dynamic test case

This test case is a simplified compressor blade model, which is in fact a cylindrical panel [V2.03.102].

This test highlights the performances of the elements in dynamic behavior by using the data of frequencies and natural modes.

Dawn frequencies and natural modes are experimental values that serve as reference results.