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The focus of Engineering Mechanics is mainly on the modeling and computational analysis of various mechanics problems in modern engineering and technology. The current research areas in the Program of Engineering Mechanics include structural analysis, structural modification and reanalysis algorithm, structural dynamics, vibration theory, multiscale computation of nanosystems and biosystems, mesh generation, mesh optimization/modification, particle packing, etc.
Impacts: Over the past ten years, more than 30 scientific and engineering research projects have been finished, including several projects supported by the National Natural Science Foundation of China, and two projects supported by National Basic Research Program (973 Program) of China. Significant and substantial progress has been achieved in different research areas. Over 40 research articles have been published on international journals, including International Journal for Numerical Methods in Engineering, Computers & Structures, Journal of Computational Physics, Computer-Aided Design, Computer modeling in engineering & sciences, etc.
Members:Guoxin Cao, Pu Chen, Yongqiang Chen, Shuixiang Li, Jianfei Liu, Moubin Liu, Shuli Sun
Listed below are selected research achievements in the Program of Engineering Mechanics.
a)      New direct reanalysis algorithm for structural modification
A new updating approach for structural modification, either non-topological or topological for static and dynamics finite element analysis has been proposed. The key concept lies on the binary tree characteristics of the global stiffness matrix derived by a graph partitioner as fill-ins’ reducer. Numerical examples show that the proposed algorithm improves reanalysis efficiency tremendously, especially for high-rank structural modification. This research can be applied to material nonlinearity, topological optimization, construction sequence analysis etc. and might causes a revolutionary advances in those analyses with step-by-step structural modification.
b)     Multiscale computation of nanosystems and biosystems
In general, the meachnical response nano-/bio-systems are much more complicated than that of the traditional material systems. The mechanical behavior of the above complex systems is investigated based on multiscale methods. In the numerical simulations, the methods are focused on the combination of density functional theory, molecular dynamic simulation and finite element modeling. In the experiments, the nanoindentation technique based on Atomic Force Microscopy (AFM) and commercial nanoindenter is one of the main tools to determine the mechanical behavior of materials at small scale.
c)      Quasi-random packing of tetrahedra
A new order metric for tetrahedral particle packings which is observed having a strong linear correlation with the packing density has been presented. The concept of quasi-random packing to represent the hierarchical random packing structure of clusters is proposed. The nematic order of clusters can be used to classify the ordered and disordered packings of tetrahedral is found, which is also an indicator for the quasi-random packing.

Figure 4.1 Left: The central cubic region with 10,121 particles in the packing system of 100,000 tetrahedral particles with the packing density of 0.809. Jointed particles are in green, and blue ones are isolated particles; right: clusters of wagon wheel in the packing, they are in a random configuration. (Li et al., Soft Matter, 9: 9298-9302, 2013)
d)     Mesh generation and optimization
A 3D mesh generation system has been developed based on the original idea of creating nodes in sphere packing way, which now has more than a hundred related papers published by over 20 researchers. A new way called SPR (small polyhedron reconnection) to improve mesh quality and maintaining conformity between mesh and geometry models has also been presented. An efficient code for a very fundamental problem in mesh generation, testing if a point is in a polyhedron, is published, which is much faster than other open codes for handling large-scale problems.

Figure 4.2 Finite element meshes generated by sphere packing method. (Liu et al., International Journal for Numerical Methods in Engineering, 79, 1004-1018, 2009)
e)      Mesh deformation and modification
A novel approach based on barycentric coordinates interpolation for mesh deformation and modification has been developed to obtain high quality discretized mesh for numerical analysis of complicate structures. This research can be applied to mesh quality optimization, dynamic grid in CFD, mesh deformation, and mesh generation for complex media, such as fractured network system, 3D braided composite, biological tissue, etc.

   Figure 4.3 Left: Mesh of 2D fractured network system, red line segments represent fractures; right: Mesh of 3D fractured network system (Tetrahedrons around fractures are displayed for clarily). (Sun et al., Mathematical Problems in Engineering, 2013)
Address: Mechanics Building, Peking University, Beijing, China Zip: 100871 Phone: +86-10-62753257 Fax: +86-10-62753257 Email: mes@mech.pku.edu.cn