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This paper presents a modified concrete damage plasticity model (CDPM) for passively confined concrete within the concrete damage plasticity theory frame in ABAQUS. The modified CDPM can be used to simulate concrete under non-uniform passive confinement, for example, Fiber-reinforced polymer (FRP)-confined square concrete columns. The modification of CDPM includes a flow rule and a strain hardening/softening criterion in which dilation angle and yield stress are important parameters. Based on the true-triaxial experiment results of passively confined concrete, the dilation angle and yield stress were determined considering different confinement stiffness and non-uniform confinement stiffness ratio. Finally, the modified CDPM were incorporated in the ABAQUS model. The prediction of the finite element model of FRP-confined square concrete columns shows good prediction accuracy.

Modular design is an important design method in the mass customization for manufacturing industry. The purpose of this paper is to meet diverse market demands while reducing the impact of products on the ecological environment. Firstly, aiming at the product life cycle process, this paper summarizes the problems encountered in each stage of the product, and introduces five green product module partition principles. Then, through the component correlation matrix, the resource greenness objective function based on the whole life cycle and the polymerization degree objective function based on the component correlation matrix are established respectively by the axiomatic design theory which makes the product mapping from functional domain to structural domain. Next, an improved artificial bee colony algorithm is proposed. Based on the artificial bee colony algorithm, the algorithm applies congestion strategy and fast nondominated sorting strategy to solve the module partition problem of product platform with multi-objective optimization, and a uniformly distributed pare to solution set is generated. Through above steps, the optimization results of module partition are obtained. Finally, an application example of aircraft tail horizontal stabilizer parts is given, and the advantages of the algorithm are proved by comparing with other algorithms.