As RWCE algorithm is used to optimize heat exchanger networks, the existence of fixed investment cost makes it difficult to produce and retain heat exchanger units with small loads. It makes structures that have not yet fully evolved be eliminated too early. We established a relaxation method of fixed investment cost. The fixed investment cost and the heat exchange of heat exchange unit are processed according to their variation. With heat exchange of heat exchange unit, relaxation strength in optimization process is adjusted in real time to guide and promote the smooth generation and evolution of small load heat exchange unit, so as to enhance structural evolution ability of heat exchange network. The relaxation strategy is applied to 9SP and 15SP examples to verify that the relaxation strategy promotes structural evolution effectively and improves optimization quality. The optimal results (2 903 528 ＄ ·a^-1, 5 115 061 ＄ ·a^-1) are better than those in literatures.

An evolutionary algorithm of multi-directional compulsive search strategy for dominant individuals is proposed to evaluate the health of global search of current population by examining individual difference index.When the optimization results stagnate for a long time, the health index becomes worse and the multi-direction forced search strategy of the dominant individual is started to expand the search direction of the dominant individual near the local optimal solution region, so as to ensure the global search ability of the algorithm.The strategy was applied to 15SP and 20SP calculation examples and results were compared with optimal results in the literature.They are decreased by 1.09% and 0.83%, respectively.It in dicates that the dominant individual multi-directional compulsive search strategy exerts fully the evolutionary potential of the dominant individual and improves the optimization efficiency of the algorithm.

A mathematical model for numerical simulation of 2D water-oil phase reservoir concerning start-up pressure gradient is solved with full implicit finite difference scheme. A reduced-order model is established by projecting original model in low dimension space formed by basis functions, which is produced from collected snapshots; CVT-Lloyd algorithm is employed in cluster analysis to tackle with flaws from collecting snapshots of same time interval. Computational results show that reduced-order model established based on POD is able to approximate the original model effectively. With cluster analysis, data reduction is eliminated, which could create uniform snapshots in space resulting in enhanced accuracy of reduce-order model. On the other hand, extremely limited clustering groups may lead to loss of information and thus impairing accuracy of reduced-order model.

Boundary element method (BEM) is used to study propagation of crack under loading. First, all leading unknown coefficients in Williams series expansion and complete stress field for notched structures are calculated with BEM and former eigenanalysis for notch tip region. Then, with consideration of non-singular stress term and maximum circumferential stress criterion of brittle fracture, crack initiation extended direction from crack tip in a semicircular bending specimen is determined by BEM. Strategy for BEM tracking crack propagation is given. Numerical examples show that the method is correct and effective in simulating propagation of plane crack.

Based on asymptotic extension of displacement field at a composite notch tip, equilibrium equation for a notch subjected to anti-plane loading is transformed into a characteristic differential equation respects to notch singularity orders. A transformation is applied to convert the equation into a set of characteristic linear ordinary differential equations. Interpolate matrix method is introduced to solve the equations for getting notch singularity orders. A single material notch, a bi-material notch and a notch terminated at bimaterial interface are studied successively. Examples indicate that the method provides all stress singularity orders synchronously. Though singular stress state is not shown with regard to non-singular orders, non-singular stress orders are indispensable parameters as evaluating complete stress field at notch tip region.

Node placement method with bubble simulation can generate high-qualify node sets in complex domains.However,its efficiency needs to be increased.Several modifications were done to reduce the cost of simulation.Firstly,let viscosity coefficient c gradually increases instead of being taken as a constant.It speeds up convergency.Moreover,at the end of each round simulation,in which bubbles additions or deletions are operated,c is assigned to a small value in order to ensure quality of bubble distribution.Secondly,as solving ordinary differential equations that control movement of bubbles,a low order numerical algorithm is chosen.Finally,sort process of overlapping rate of bubbles is removed.It is replaced by setting only threshold for bubbles additions and deletions.Numerial examples show that computing cost decreases by approximately 40% and average quality of Delaunay triangulation corresponding to node set is over 0.9.It shows that the algorithms are efficient and generate node sets with high-quality.

For mesh generation of a two-parameter surface, anisotropic and non-uniform node placement method with bubble simulation is applied to optimize node distribution in parameter area. Then the parameter area is meshed with constrained Delaunay triangulation. Finally, according to the mapping method, two-parametric surface mesh is obtained. A second order Riemann metric tensor determines distribution of nodes in the parameter area. It could be co-generated with a three-dimensional surface metric tensor and gradient of surface functions. Numerical examples show that the node placement method with bubble simulation can generate node set meeting requirements of Riemann metric in parameter area. Nodes are meshed and mapped back into the surface. A high quality surface mesh is obtained.

Dynamics of a pair of voids located along loading direction under uniaxial tension is investigated using molecular dynamics method.Size effects in void growth and coalescence are studied.It shows that different-sized voids grow and coalesce through dislocation nucleating on void surfaces.In early elastic stage,voids grow along loading direction,then along vertical direction and finally form octahedral-like structures in plastic stage.Critical yield stress increases with decreasing of void size.If radius is large,dislocations nucleate and migrate symmetrically.Voids elongate in loading direction,and evolution process is similar.If radius is small,dislocations nucleate asymmetrically and voids elongate along vertical direction.The process of void growth may be characterized by elastic deformation,independent growth,coalescence and steady growth.Independent growth stage diminishes gradually as void size becomes smaller.

A method of mutual coupling and circulating iteration is presented to evaluate the thermal resistance and thermal capacity network of unit (differential) sections and separate joint points for the solar energy collecter system based on the model proposed by the second writer of this paper.