Based on the two problems associated with numerical simulation for concrete material zero consumption of energy and mesh dependence in the classical local damage model, the implicit gradient damage model is introduced.

Soft behaviors always occur in rock and soil engineering, however, the mesh-dependence will be caused when traditional elastoplastic finite element method is applied in shear bands problems with soft behavior.

Combined with density filtering technique to improve the smoothness of density field,the mesh-dependence phenomenon is overcome.

In order to overcome numerical instabilities such as checkerboards,mesh-dependence and gray regions in the topological optimization of continuum structures,a perimeter-constrained version of the nodal independent continuous mapping method with variational upper-bound is proposed.

This paper makes use of the IGES file of the KVLCC2M model hull to validate the software\'s robustness and the grid dependence research of CFD drag prediction and maneuverability prediction is carried out.

The different results built on different parameters are compared,and the mesh dependence,constrains dependence and computing efficiency of topology results are also discussed.

The two problems associated with strain softening of concerte material,zero consumption of energy and mesh dependence,are studied.

The two problems associated with strain softening of concrete material—zero consumption of energy and mesh dependence are studied.