Long Kai

North China Electric Power University | NCEPU · Department of Electrical Power Engineering

This paper incorporates the homogenization theory into non-penalized Smooth-Edged Material Distribution for Optimizing Topology (SEMDOT) algorithm to conduct the design of cellular structures with the maximum shear modulus. The parametric study and comparison with existing results obtained by BESO are carried out. The numerical examples in 2D and 3...

Although the flexible origami gripper can handle a wide range of objects, there is a need for significant further improvement in its gripping performance. This study develops a novel nonlinear topology optimization (NTO) method to enhance the gripping performance of an origami chomper-based flexible gripper. The proposed NTO method incorporates the...

This paper proposes a topology optimization methodology for offshore wind turbine (OWT) jacket structure design in the concept phase. First of all, modal analysis and load calculation of a 5 MW reference OWT are performed. On the basis of finite element analysis, the displacement and von Mises stress of multi-jacket support structures in various ul...

This article proposes an augmented Lagrangian-based topology optimization approach to minimize the volume fraction subject to multiple nodal displacement constraints. The proposed method puts the multiple constraint equations in the objective function and transforms it into a sequence of unconstrained optimization problems. This study explains the...

The objective of this work is to build a useful-response-surface-based reliability design approach for solving stress-constrained optimization problems taking into consideration load uncertainty. To this end, a reliability optimization problem of minimizing the volume fraction while satisfying a global probabilistic stress constraint is formulated,...

Density-based topology optimization algorithms, such as solid isotropic material with penalization (SIMP), pursue solid/void solutions to yield distinct topologies, however blurry or zigzag boundaries are unavoidable. By contrast, newly developed elemental volume fraction based algorithms pursue solid/void grid points, and the intermediate elements...

The extreme deformation control under transient excitation typically takes the forms of bounds in the time domain. These maximum constraints are typically addressed using an aggregation strategy that approximates the upper bound in a differentiable manner. However, the conventional aggregation method exhibits a dependence on specified parameters. I...

Currently, most works on synchronous optimization of composite topology and fiber orientation are all carried out under deterministic conditions, where the influence of uncertain factor on design optimization of fiber-reinforced composite structures is ignored. In this work, an effective probabilistic reliability-based topology optimization (RBTO)...

The existing wind turbine vortex-vibration researohes usually focus on the first-order vortex-induced vibration of the rigid tower regardless of the top mass instead of ignoring. The second-order vortex-induced vibration of the high-flexible tower with top mass is neglected. This study mainly concentrates on the second- order vortex-induced vibrati...

This work integrate functional gradient constraint into multi-material topology optimization for transient heat conduction structure, taking into account the use of ordered rational approximation of material properties to represent the multi-material interpolation model. The optimization objectives modeled by the aggregation function are to minimiz...

Origami-based metamaterial has shown remarkable mechanical properties rarely found in natural materials, but achieving tailored multistage stiffness is still challenging. We propose a novel zigzag-base stacked-origami (ZBSO) metamaterial with tailored multistage stiffness based on crease customization and stacking strategies. A high precision finit...

The effect of power curtailment，which is ignored by the existing fatigue life prediction methods of tower bolt，is considered in this study. Firstly，the time series load of wind turbines under various power curtailment conditions is obtained by GH Bladed software. Secondly，the Schmidt-Neuper algorithm and the linear cumulative damage theory are appl...

Topology optimization is a powerful tool having capability of generating new solution to engineering design problems, while these designs enhance manufacturability and reduce manufacturing costs in a computational setting. Mesh-independent convergence and other techniques have been widely used as topology optimization technique, but they produce gr...

Cellular structure can possess superior mechanical properties and low density simultaneously. Additive manufacturing has experienced substantial progress in the past decades, which promotes the popularity of such bone-like structure. This paper proposes a methodology on the topological design of porous structure. For the typical technologies such a...

This article proposed a methodology that combines two well-known projections and modified density-based optimized techniques in one formulation methodology. This methodology contains an effective explicit geometric entity identified by shape variables that provide easy control in desired particular regions; implicit density-based topological optimi...

Origami-baed metamaterial has shown remarkable mechanical properties rarely found in natural materials, but achieving tailored multistage stiffness is still a challenge. This study proposes a novel zigzag-base stacked-origami (ZBSO) metamaterial with tailored multistage stiffness property based on crease customization and stacking strategies. A hig...

This paper proposes a novel method for the continuum topology optimization of transient vibration problem with maximum dynamic response constraint. An aggregated index in the form of an integral function is presented to cope with the maximum response constraint in the time domain. The density filter solid isotropic material with penalization method...

This article presents a novel formulation for geometric nonlinear topology optimization problems. In practical engineering, maximum deflection is frequently used to quantify the stiffness of continuum structures, yet not applied generally as the optimization constraint in geometrically nonlinear topology optimization problems. In this study, the ma...

Graph theory is a subdivision of discrete mathematics. In graph theory, a graph is made up of vertices connected through edges. Topological indices are numerical parameters or descriptors of graph. Topological index tells the symmetry of compound and helps us to compare those mathematical values, with boiling point, melting point, density, viscosit...

Topological index sometimes called molecular descriptor is a numerical value which associates a chemical composition for correlating chemical structure with numerous physical properties, chemical reactivity, or biological activity. In this paper, we study some topological indices of boron and try to correlate the physicochemical properties such as...

A methodology for achieving the maximum bulk or shear modulus in an elastic composite composed of two isotropic phases with distinct Poisson’s ratios is proposed. A topology optimization algorithm is developed which is capable of finding microstructures with extreme properties very close to theoretical upper bounds. The effective mechanical propert...

Currently, most works on layout optimization problem of continuum structure embedded with movable holes are all carried out to maximize the stiffness of the overall system. In this work, the embedding problem is solved for minimum stress design for the first time. To this end, we propose an effective hybrid methodology under SIMP-based computationa...

This paper proposes a new methodology for continuum topology optimization that is capable of fatigue-resistance design. Firstly, penalized stress is adopted to circumvent the singularity issue. Secondly, another additional penalization formulation of the elemental fatigue damage is proposed. The quasi-static finite element method is performed to ca...

Compared with traditional metal-materials, fiber-reinforced composite materials have better performance in many aspects such as strength, stiffness, and fracture resistance. At present, fiber-reinforced composite materials have been widely used in automotive, aerospace, and other industrial fields. This paper proposes a topology optimization method...

In this article, an explicit topology optimization method is proposed for maximizing the overall stiffness of a multi-material continuum structure embedded with multiple variable-size movable holes based on the Moving Morphable Bars (MMB) method. To this end, multiple sets of morphable bars are used to describe the structural topology of multiphase...

Purpose Negative Poisson’s ratio (NPR) material has huge potential applications in various industrial fields. However, lower Young’s modulus due to the porous form limits its further applications. Based on the topology optimization technique, this paper aims to optimize the structure consisting two isotropic porous materials with positive Poisson’s...

Nowadays, various regions and financial institutions in China are launching a new round of financial innovation in order to gain the next round of competitive advantages. As a pioneer of China’s reform and opening-up, Shenzhen must naturally consider what principles should be followed in financial innovation, what model should be adopted, what timi...

Scientists and researchers are focusing on generation electrical energy using maximum share of renewable energy resources. Wind turbines possess crucial part in generation of electrical energy from renewable energy sources. A lot of research work has been carried out to find out optimum mechanical design of wind turbines specially focused on reduct...

This paper introduces a new formulation of topology optimization for robust design including local failure and load uncertainty. In contrast to most studies, the focus has been on minimizing the total volume with multiple compliance constraints. With the introduction of the reciprocal intermediate variables, the topology optimization problem can be...

In this paper, we develop an efficient diagonal quadratic optimization formulation for minimum weight design problem subject to multiple constraints. An high‐efficiency computational approach of topology optimization is implemented within the framework of approximate reanalysis. The key point of the formulation is the introduction of the reciprocal...

In this paper, we propose a method for stress-constrained topology optimization of continuum structure sustaining harmonic load excitation using the reciprocal variables. In the optimization formulation, the total volume is minimized with a given stress amplitude constraint. The p-norm aggregation function is adopted to treat the vast number of loc...

Purpose The optimal material microstructures in pure material design are no longer efficient or optimal when accounting macroscopic structure performance with specific boundary conditions. Therefore, it is important to provide a novel multiscale topology optimization framework to tailor the topology of structure and the material to achieve specifi...

Structures and/or materials with engineered functionality, capable of achieving targeted mechanical responses reacting to changes in external excitation, have various potential engineering applications, e.g. aerospace, oceanographic engineering, soft robot, and several others. Yet tunable mechanical performance is normally realized through carefull...

Negative Poisson’s ratio (NPR) material attracts a lot of attentions for its unique mechanical properties. However, achieving NPR is at the expense of reducing Young’s modulus. It has been observed that the composite stiffness can be enhanced when blending positive Poisson’s ratio (PPR) material into NPR material. Based on the respective interpolat...

Layout design of multi-component systems has received ever-increasing attention over recent years. However, most of the current literature on the layout design of multi-component systems conducted are all carried out in an implicit way. In this paper, an explicit optimization model based on the moving morphable bars method is proposed. To this aim,...

It is necessary to limit maximum nominal stress for engineering structural design generally, so as to avoid that the failure of fracture or fatigue occurs. Topology optimization approach is a feasible strategy. The conventional bi-evolutionary structural optimization (BESO) method cannot effectively address the topology optimization problem with st...

It is revealed that the local optimum is particularly prone to occur in multi-material topology optimization using the conventional SIMP method. To overcome these undesirable phenomena, reciprocal variables are introduced into the formulation of topology optimization for minimization of total weight with the prescribed constraint of various structu...

Purpose In pure material design, the previous research has indicated that lots of optimization factors such as used algorithm and parameters have influence on the optimal solution. In other words, there are multiple local minima for the topological design of materials for extreme properties. Therefore, the purpose of this study is to attempt differ...

Transient heat conduction analysis involves extensive computational cost. It becomes more serious for multi-material topology optimization, in which many design variables are involved and hundreds of iterations are usually required for convergence. This article aims to provide an efficient quadratic approximation for multi-material topology optimiz...

The present work introduces a novel concurrent optimization formulation to meet the requirements of lightweight design and various constraints simultaneously. Nodal displacement of macrostructure and effective thermal conductivity of microstructure are referred as the constraint functions, which means taking into account both the load-carrying capa...

Most studies on composites assume that the constituent phases have different values of stiffness. Little attention has been paid to the effect of constituent phases having distinct Poisson’s ratios. This research focuses on a concurrent optimization method for simultaneously designing composite structures and materials with distinct Poisson’s ratio...

In topology optimization problems of structures containing multiphase materials, it is common practice to set the volume constraint of each constituent phase or total mass of entire constituent phase constraint to control the final material usage. On the practical engineering background for lightweight design, it is of significance that the minimiz...

This paper introduces a two-scale concurrent topology optimization method for maximizing the frequency of composite macrostructure that are composed of periodic composite units (PCUs) consisting of two isotropic materials with distinct Poisson’s ratios. Interpolation of Poisson’s ratios of different constituent phases is used in PCU to exploit the...

This paper presents a concurrent topology optimization approach for simultaneous design of composite structures and their periodic material microstructures with three or more phases. The effective properties of multi-phase materials are obtained via homogenization technique which serves as a bridge of the finite element models of the macrostructure...

This article introduces thermal conductivity constraints into concurrent design. The influence of thermal conductivity on macrostructure and orthotropic composite material is extensively investigated using the minimum mean compliance as the objective function. To simultaneously control the amounts of different phase materials, a given mass fraction...

For achieve the anti-fatigue strength design of the tower flange's bolts for the large-scale horizontal axis wind turbines, the checking method of fatigue strength was proposed based on the Schmidt-Neuper model. According to the stiffness distribution ratio of single sector flange system, the nonlinear relationship of internal force-external tensio...

Recent studies have shown that the stiffness of composites in one or more directions could increase dramatically when the Poisson’s ratios of constituent phases approach the thermodynamic limits. In this paper, we establish a computational framework for the topology design of the microstructure of a composite material whose constituent phases have...

This paper presents a hierarchical topology optimization method to simultaneously achieve the optimum structures and multiphase material cells for minimum system thermal compliance. Macro design variables and micro phase design variables are introduced independently, and coupled through elemental phase relative density. Based on uniform interpolati...

In order to realize the buckling strength design for the opening door of the large-scale horizontal axis wind turbine tower, the method combined with the engineering method and the FEM was presented. The FE model of the door was established. The first-order buckling eigenvalues and buckling modes for three different structures were calculated and a...

To improve the convergence for topology optimization of continuum structure, a new material interpolation model is proposed. This function curve parameterized by certain penalty is similar to solid isotropic microstructures with penalization (SIMP) curve. In static topology optimization problem, the new interpolation function maintains the advantag...

Based on homogenization theory, hexagonal microstructure with isotropic behavior is adopted as description of the macroscopic material. A new topological optimization method of continuum structure for dynamic problems is presented based on continuous size field. The proper character of the microcosmic cell is numerically validated to avoid localize...

To resolve the numerical instabilities in continuum topology optimization, nodal topological variables are adopted to describe the existence or null of elements combined with independent continuous mapping method. Young's module and volume of the element are calculated by independent topological variable fields. Based on the lower order element sha...

The independent continuous mapping(ICM) method is integrated into element free Galerkin method and a new implementation of topology optimization for continuum structure is presented. To facilitate the enforcement of the essential boundary condition and derivative of various sensitivities, a singular weight function in element free Galerkin method i...

To overcome various kinds of numerical instabilities in topology optimization for compliant mechanisms, a method using material point topological variables as design variables is proposed. The material point topological variable can be viewed as natural extension of the nodal density. Based on a modified mesh-independent filtering scheme, a new int...

Optimal cross-section design of beams plays a distinctive role which involve the rigidity of the member in bending, shear and torsion load conditions. Practically modern overhead crane girders, railway bridge girders or rail tracks etc. require constant cross-section along the axial direction as the load location changes all the time. Conventional...

Computation of the energy release rate (G) based on the virtual crack closure technique (VCCT) and finite element method is presented. The process is really redundancy when calculating the G value by processing the results of finite element method. However, the VCCT method can be implemented into finite element software by developing the interface...

In order to overcome numerical instabilities such as checkerboards, meshdependence in topology optimization of continuum structures, a new implementation combined with homogenization method without introducing any additional constraint parameter is presented. To overcome the shortcoming of continuous material distribution by the introduction of fin...

A new node-based independent continuous mapping method for topological optimization of continuum structures is presented. Modifying the previous ICM method, the element-based topological variables is replaced by node-based topological variables which illustrate the features of every element. Continuity of topological variables is ensured by interpo...

This paper presents a new approach to the structural topology optimization of continuum structures. Material-point independent variables are presented to illustrate the existence condition, or inexistence of the material points and their vicinity instead of elements or nodes in popular topology optimization methods. Topological variables field is c...

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. In order to avoid the determination of value of the perimeter const...

To investigate the factors and methods to extract clear configuration in the topological optimization of continuum structure, a topological optimization model using nodal density as the design variable is established. Checkerboard patterns are naturally avoided based on the continuous density field. Combined with density filtering technique to impr...

A new methodology for main bearing cap design was presented based on topological optimization and shape optimization. In topological optimization, filter functions of elements with respect to the unit volume and stiffness matrices were selected based on RAMP interpolation scheme. In shape optimization, efficient derivatives have been obtained by us...

A new topological optimization method of dynamic continuum structures is presented based on nodal independent design variables. Topological optimization models are developed where dynamic structural responses are taken as objective and prescribed volume fraction are referred to as constraint conditions. Image-filtering method is adopted to eliminat...

A multi-objective programming scheme for continuum topology optimization is proposed, in which both compliance, displacement of nodes and eigenfrequency are regarded as static and dynamic optimization objectives, respectively. Node-based independent variables which ensure continuity in design domain are taken as design variables. The method is immu...

Heat energy, temperature and sum of square of temperature in local domain were taken as global, local and regional measures independently in topological optimization of continuous structure for heat conduction. Their sensitivities were derived by using adjoint method. Based on comparison between displacement field and temperature field, structural...

Some sensitivity analysis methods in continuum shape optimization were summarized. To overcome difficulty of high computational cost in difference sensitivity analysis, efficient derivatives were obtained using 'approximate-difference' strategy based on combined approximation method for static and mode analysis and accurate sensitivity was ensured...

Due to the independence of design variables in independent, continuous, mapping (ICM) method, a new mixed modeling method was presented. SIMP and RAMP interpolation schemes were used as filter functions of element and volume element stiffness matrix. Based on mutual combination of filter functions, four different topological optimization models