L.X. Li

An improved collaborative optimization for multidisciplinary problems with coupled design variables

Abstract In this paper, the collaborative optimization is improved to tackle multidisciplinary problems with coupling design variables within disciplines. The design variables are first distinctly classified into private and public ones according to disciplines. A criterion is then proposed to judge the coupling of private variables with the public variables. For the coupling case, a strategy is suggested to decouple the variables before performing the collaborative optimization. To demonstrate the effectiveness of the improved collaborative optimization, two practical optimization problems are comparatively studied for uncoupled design variables as well as coupled ones. It is shown that the present framework can achieve the better optimal results as compared with other methods. Furthermore, the judge criterion and the decoupling strategy are also validated.

A collaborative optimization framework for parametric and parameter-free variables

Purpose – The purpose of this paper is to improve the framework of classical collaborative optimization (CCO) so as to solve the multi-disciplinary optimization problems with parametric and parameter-free variables, and therefore an improved collaborative optimization (ICO) is proposed. Design/methodology/approach – To clarify the relation of design variables, the optimization problem is classified into three general case. For each case, the respective treatment is suggested for coupled or uncoupled variables in the framework of the ICO. Findings – The decoupling treatment suggested in the ICO framework not only avoids the iteration divergence and thus optimization failure, but increases the optimal design space to some extent. The method is validated by optimizing an aircraft assembly and a high-speed train assembly. Originality/value – The two practical examples proves that the present ICO succeeds in solving the problem that the CCO failed to, also gives the optimal results better than those from the s...

THE UNIFIED SOLUTION FOR A BEAM OF RECTANGULAR CROSS-SECTION WITH DIFFERENT HIGHER-ORDER SHEAR DEFORMATION MODELS

The unified solution is studied for a beam of rectangular cross section. With the rotation defined in the average sense over the cross section, the kinematics with higher-order shear deformation models in axial displacement is first expressed in a unified form by using the fundamental higher-order term with some properties. The shear correction factor is then derived and discussed for the four commonly used higher-order shear deformation models including the third-order model, the sine model, the hyperbolic sine model and the exponential model. The unified solution is finally obtained for a beam subjected to an arbitrarily distributed load. The relation with that from the conventional beam theory is established, and therefore the difference is reasonably explained. A very good agreement with the elasticity theory validates the present solution.

An improved finite element method for cracks with multiple branches

The conventional finite element method is improved to tackle complex cracks with multiple branches. The parasitic nodes are introduced to the nodes whose nodal support is completely cut by the crack surfaces, while the nodes whose supports contain crack tips inside are accordingly enriched by the crack tip functions. The principle to set parasitic nodes is regulated, and the relation to the previous methods is dissected. The formulation of the present method is derived, and numerical experiments are conducted. The results show that the present method can treat complex cracks conveniently and efficiently, and the unknowns have a clear physical interpretation.

Applicability of hierarchical fiber bundle materials to mechanical environments

Biomaterials use a hierarchical structure to optimize their self-healing behavior, for instance. However, the behavior may be constrained under different mechanical environments. In this paper, a system is suggested that the mechanical environment is modeled as a spring connected in series with the fiber bundle material. For the spring, the elastic behavior with stiffness is obeyed while, for the fiber bundle material, the nonlinear elastic constitutive relation is obeyed according to the Weibull distribution and the Daniels’ theory. Relying on the principle of total potential, the applicability condition is proposed for the system and the critical stiffness is thus derived for the spring. The applicability of hierarchical fiber bundle materials is finally investigated. The results show that the hierarchy can significantly change the critical stiffness, and hence demonstrates quite different applicability to a given mechanical environment.

A Two-Scale Approach to Numerically Predict the Strength and Degradation of Composites

Regarding the composite structure firstly as a composite on the macro-scale and then as the fiber phase and matrix phase on the meso scale, a two-scale approach is proposed to numerically predict the strength of fiber-reinforced composites. As the first step, the stress field is calculated by combining the macro-scale and meso-scale analysis together. With the stress field, the strength index is defined and the initial strength is then predicted. As the second step, the damage is defined and the degradation strength is then predicted. The two-scale approach is validated by analyzing a woven fiber reinforced composite under compression after impact (CAI) loading. Compared with the conventional homogenization approach, the present two-scale approach can not only calculate the stress and the damage of constituent phases on the meso scale, but obtain well correlated CAI strengths with the experimental test.

A key-node finite element method and its application to porous materials

Abstract Due to the complex microstructures of porous materials, the conventional finite element method is often inefficient when simulating their mechanical responses. In this paper, a key-node finite element method is proposed. First, the concept of key-node is introduced over the element level, and then the governing equations are theoretically derived and corresponding boundary conditions for shape functions of key-node finite element are prescribed. The key-node finite element method is finally established by following the procedure of conventional finite element method to numerically solve the shape functions. Including the information of micro-structures and physical details in shape functions, the key-node finite element is more efficient when preserving a high accuracy, which is validated by typical applications to elastic and elasto-plastic analyses of porous materials. It is straightforward to extend the present method to the three-dimensional case or to solving more challengeable problems such as dynamical responses with high frequencies.