Plate/shell topological optimization subjected to linear buckling constraints by adopting composite exponential filtering function

In this paper, a model of topology optimization with linear buckling constraints is established based on an independent and continuous mapping method to minimize the plate/shell structure weight. A composite exponential function（CEF） is selected as filtering functions for element weight, the element stiffness matrix and the element geometric stiffness matrix, which recognize the design variables, and to implement the changing process of design variables from“discrete” to “continuous” and back to “discrete”. The buckling constraints are approximated as explicit formulations based on the Taylor expansion and the filtering function. The optimization model is transformed to dual programming and solved by the dual sequence quadratic programming algorithm. Finally, three numerical examples with power function and CEF as filter function are analyzed and discussed to demonstrate the feasibility and efficiency of the proposed method.

Size and Dynamics of Ring Polymers under Different Topological Constraints

The impact of ring polymer length N and the influence of interchain and intrachain interactions on the size and dynamic behaviors of ring polymers,including the structural relaxation time τ_(R) and self-diffusion coefficient D,remain poorly understood at present due to a lack of systematic studies with relatively large N values.This work addressed this issue by applying dynamic Monte Carlo simulations with independently tuned interchain and intrachain interactions to investigate the size and dynamics of the ring melts with chain lengths over a wide range of 0.2N_(e)≤N≤80N_(e)(N_(e) is the entanglement length of corresponding linear chains)under different topological constraints,including all-crossing and intercrossing systems.We found that it was inappropriate to treat the unknotting constraint free energy of the ring chains in the melts as the free energy contributed by the excluded volume interactions of polymers in a good solvent.Scaling exponents of 2.5 and 1.5 reflecting the Ndependence of τ_(R) were obtained for long ring chains in non-crossing and intra-crossing systems,respectively,suggesting that the ring chains behaved as individual clusters and exhibited Zimm-like dynamics in intra-crossing systems.A single scaling exponent of-2 reflecting the Ndependence of D was obtained for ring chains in non-crossing and intra-crossing systems,indicating that the intrachain constraints affected only the value of D,and had little influence on the scaling relationship between D and N.Furthermore,the extended Stokes-Einstein relation broke down for the ring chains in the non-crossing and intra-crossing systems because the structural relaxation and translational diffusion were decoupled for the short ring systems,while both the translational diffusion and rotational relaxations,as well as diffusion at short and long time scales,were decoupled for long ring systems.

A DIRECTED GRAPH ALGORITHM OF VARIATIONAL GEOMETRY BASED ON GEOMETRIC REASONING

The undirected graph to express engineering drawings is discussed .The principle to re-solve and reason the undirected graph is presented, and the algorithm finally transforms theundirected graph into the resolvable directed graph. Therefore,a rapid and simple way is suppliedfor variational design. A prototype of this algorithm has been implemented, and some examplesare given.

Stiffeners layout design of thin-walled structures with constraints on multi-fastener joint loads

The purpose of this paper is to present an extended topology optimization method for the stiffeners layout design of aircraft assembled structures. Multi-fastener joint loads and manufacturing constraints are considered simultaneously. On one hand, the joint loads are calculated and constrained within a limited value to avoid the failure of fasteners. On the other hand, the manufacturing constraints of the material distribution in the machining directions of stiffeners are implemented by an improved piecewise interpolation based on a beveled cut-surface. It is proven that the objective function is strictly continuous and differentiable with respect to the piecewise interpolation. The effects of the extended method with two different constraints are highlighted by typical numerical examples. Compared with the standard topology optimization, the final designs have clearly shown the layout of stiffeners and the joint loads have been perfectly constrained to a satisfying level.

Coil to globule transition of homo- and block-copolymer with different topological constraint and chain stiffness

In this paper, we present the coil-to-globule(CG) transitions of homopolymers and multiblock copolymers with different topology and stiffness by using molecular dynamics with integrated tempering sampling method. The sampling method was a novel enhanced method that efficiently sampled the energy space with low computational costs. The method proved to be efficient and precise to study the structural transitions of polymer chains with complex topological constraint, which may not be easily done by using conventional Monte Carlo method. The topological constraint affects the globule shape of the polymer chain, thus further influencing the CG transition. We found that increasing the topological constraint generally decreased CG transition temperature for homopolymers. For semiflexible chains, an additional first-order like symmetry-broken transition emerged. For block copolymers, the topological constraint did not obviously change the transition temperature, but greatly reduced the energy signal of the CG transition.

An improved probabilistic relaxation method for matching multi-scale road networks

Matching multi-scale road networks in the same area is the first step in merging two road networks or updating one based upon the other.The quality of the merge or update depends greatly on the matching accuracy of the two road networks.We propose an improved probabilistic relaxation method,considering both local and global optimizations for matching multi-scale of road networks.The aim is to achieve local optimization,as well as to address the identification of the M:N matching pattern by means of inserting virtual nodes to achieve global optimization effects.Then,by adding two attribute-related evaluation indicators,we developed four evaluation indicators to evaluate the matching accuracy,considering both geographic and attribute information.This paper also provides instructions on how to identify the proper buffer threshold during matching procedures.Extensive experiments were conducted to compare the proposed method with the traditional approach.The results indicate that:(1)the overall matching accuracy of each evaluation indicator exceeds 90%;(2)the overall matching accuracy increases by 6–12%after an M:N matching pattern is added,and by 4–6%following the addition of topology indicators;and(3)the proper buffer threshold is about twice the average value of the closest distance from all nodes.

Force-Extension Curve of an Entangled Polymer Chain:A Superspace Approach

The statistical mechanics of an ideal polymer chain entangled with static topological constraints is studied using a superspace approach,in which the probability distribution of the polymer is obtained as solutions of the Fokker-Planck equation in a superspace with an inner structure characterized by the n-generator free group.The theory predicts that the force-extension curve of the polymer under the topological constraints has the generic form F=kl+Z/l,where l is an effective extension.Aside from the elastic term that is linear in l,the forceextension curve contains a universal term of the form Z/l.The magnitude of this topological term is determined by the topological charge number Z,which characterizes the topological nature of the static constraints.The theoretical results are further verified by a scaling analysis based on a blob model of the chain conformations.

The scaling behavior of the second virial coefficient of linear and ring polymer

The scaling behavior of the second virial coefficient of ring polymers at the theta temperature of the corresponding linear polymer(θ_L) is investigated by off-lattice Monte Carlo simulations. The effects of the solvents are modeled by pairwise interaction between polymer monomers in this approach. Using the umbrella sampling, we calculate the effective potential U(r) between two ring polymers as well as the second virial coefficient A_2 of ring polymers at θ_L, which results from a combination of 3-body interactions and topological constraints. The trend in the strength of the effective potential with respect to chain length shows a non-monotonic behavior, differently from that caused only by topological constraints. Our simulation suggests that there are three regimes about the scaling behavior of A_2 of ring polymers at θ_L: 3-body interactions dominating regime, the crossover regime, and the topological constraints dominating regime.