Simultaneous optimization of topology and layout of modular stiffeners on shells and plates

Stiffened shells and plates are widely used in engineering. Their performance is highly influenced by the arrangement, or layout, of stiffeners on the base shell or plate and the geometric features, or topology, of these stiffeners. Moreover, modular design is beneficial, since it allows for increased quality control and mass production. In this work, a method is developed that simultaneously optimizes the topology of stiffeners and their layout on a base shell or plate. This is accomplished by introducing a fixed number of modular stiffeners, which are subject to density-based topology optimization and a mapping of these modules to a ground structure. To illustrate potential applications, several stiffened plates and shell examples are presented. All examples demonstrated that the proposed method is able to generate clear topologies for any number of modules and a distinct layout of the stiffeners on the base shell or plate.

Static Analysis of Stiffened Shells Using an Edge-Based Smoothed MITC3 (ES-MITC3) Method

A novel approach for solving the stiffened shell structures by using an edge-based smoothed MITC3 finite element method (ES-MITC3) is presented in this paper. The ES-MITC3 method is an efficient finite element method by combining the edge-based smoothed finite element method (ES-FEM) with the original MITC3 triangular element to not only significantly improve the accuracy but also overcome the shear-locking phenomenon in the Reissner–Mindlin shell analysis. In this study, the ES-MITC3 method is applied for shell structures and then reinforced by stiffeners based on the Timoshenko beam theory to achieve more durability and strength structures. The transverse displacements of the shell structures and stiffeners at the contact positions are assumed compatible. Numerical results of the ES-MITC3 element are compared with those of available other numerical results to demonstrate a good convergence and accuracy of the present method.

On FEM analysis of Cosserat-type stiffened shells: static and stability linear analysis

The present research investigates the theory and numerical analysis of shells stiffened with beams in the framework based on the geometrically exact theories of shells and beams. Shell’s and beam’s kinematics are described by the Cosserat surface and the Cosserat rod, respectively, which are consistent including deformation and strain measures. A FEM approximation of the virtual work principle leads to the conforming shell and beam FE with 6 DoFs (including the drilling rotation for shells) in each node. Examples of static and stability linear analyses are included. Novel design formulas for the stability of stiffened shells are included.