## Verification and Validation of Beam/Plate/Shell/Multiscale Theories

Verification and validation (V&V) are important considerations for a computer simulation code. It is commonly understood that verification is to check whether a computer code solves the equations correctly while validation is to check whether a computer code solves the correct equations. Verification is about finding out whether a computer code behaves according to the underlying theory while validation is about finding out whether the underlying theory, represented by a computer code, can be used to achieve intended function. Verification is usually done by simple benchmark examples of the theory for which the code is designed to solve, while validation must be done by comparing to data generated by other means which are not from the theory underpinning the code.

It is commonly believed that experimental results should be used for validating computer simulations. If the theory is constructed to model certain physical behavior, then it makes perfect sense to validate the theory and companion computer code using physical experiments which can replicate the same physical behavior. However, for computer codes based on simplified theories which are constructed from other theories, one can argue that the original theory can be used for more direct and manageable validation.

For example, a beam/plate/shell theory is constructed out of the 3D continuum mechanics theory. Then the 3D continuum mechanics theory, which is usually solved using 3D FEA, can be used to validate the beam/plate/shell theory. A multiscale modeling approach is constructed to avoid the prohibitive computational cost of a direct numerical simulation (DNS). Then, a multiscale modeling approach can be validated by comparing to DNS to show that the multiscale approach can achieve a good approximation of DNS results with much improved efficiency. The main difficulty regarding using the original model for validation is that the computation might be impossible based on available computing hardware and software resources, for example simulating a composite rotor blade with all the fiber details. One possible way to avoid this difficulty is to create a problem which DNS is possible. For example, we can create a composite laminate with many fibers to validate a multiscale approach for fiber reinforced composites. Direct comparison of the results of computer codes based on simplified theories with experiments might be confusing sometimes because some of the physics might have not been correctly modeled in the original theory. Additional approximation introduced by simplification might add or subtract from the loss of fidelity of the original theory.