Notice of RetractionOn solving the min-max problem of the stress of the structural elements in the structural topology optimization
In this paper, we deal with the min-max problem of the stress of the structural elements in the structural topology optimization. A generalized KS function is presented which transforms the local stress to global strain energy of structure through Von Mises Criterion. The ICM method is employed for solving the topology optimization problem. Some classic numerical examples are presented which provide quality solutions and the minimum stress design to obtain the final design.
Independent continuous mapping for topological optimization of frame structures
Based on the Independent Continuous Mapping method (ICM), a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable stress and element stiffness, which transform the 0-1 type discrete topological variables into continuous topological variables between 0 and 1. Two methods for the filter functions are adopted to avoid the structural singularity and recover falsely deleted elements: the weak material element method and the tiny section element method. Three criteria (no structural singularity, no violated constraints and no change of structural weight) are introduced to judge iteration convergence. These criteria allow finding an appropriate threshold by adjusting a discount factor in the iteration procedure. To improve the efficiency, the original optimization model is transformed into a dual problem according to the dual theory and solved in its dual space. By using MSC/Nastran as the structural solver and MSC/Patran as the developing platform, a topological optimization software of frame structures is accomplished. Numerical examples show that the ICM method is very efficient for the topological optimization of frame structures.
Calyculins and Related Marine Natural Products as Serine-Threonine Protein Phosphatase PP1 and PP2A Inhibitors and Total Syntheses of Calyculin A, B, and C
Calyculins, highly cytotoxic polyketides, originally isolated from the marine sponge Discodermia calyx by Fusetani and co-workers, belong to the lithistid sponges group. These molecules have become interesting targets for cell biologists and synthetic organic chemists. The serine/threonine protein phosphatases play an essential role in the cellular signalling, metabolism, and cell cycle control. Calyculins express potent protein phosphatase 1 and 2A inhibitory activity, and have therefore become valuable tools for cellular biologists studying intracellular processes and their control by reversible phosphorylation. Calyculins might also play an important role in the development of several diseases such as cancer, neurodegenerative diseases, and type 2-diabetes mellitus. The fascinating structures of calyculins have inspired various groups of synthetic organic chemists to develop total syntheses of the most abundant calyculins A and C. However, with fifteen chiral centres, a cyano-capped tetraene unit, a phosphate-bearing spiroketal, an anti, anti, anti dipropionate segment, an α-chiral oxazole, and a trihydroxylated γ-amino acid, calyculins reach versatility that only few natural products can surpass, and truly challenge modern chemists’ asymmetric synthesis skills.