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Design Closure
Published in Louis Scheffer, Luciano Lavagno, Grant Martin, EDA for IC Implementation, Circuit Design, and Process Technology, 2018
Another key consideration in placement is design hierarchy. All of the previous design steps, i.e., concept, logic design, floorplanning, and logic synthesis, rely on hierarchy to limit problem complexity. At the placement stage it is possible to either keep the design hierarchy set at logic design, or flatten it. If the hierarchy is kept, each hierarchical unit is placed separately, and then the units are combined to form the chip. In flat design the borders between some or all logical hierarchies are dissolved and the flattened logic is placed together. Generally, flattening a design allows significantly better optimization of performance and power during placement and subsequent design steps and requires less manual effort. On the other hand, retaining all or some of the hierarchy allows better parallelization of design effort, easier reuse of design, and faster incorporation of design changes. In addition, hierarchy is a natural way to keep the highest frequency portions of a design physically compact, which can help reduce clock skew. It should be noted that some flat placement flows provide some form of move bounds mechanism to manage the proximity of the most performance-critical circuits. The debate on advantages and disadvantages of flat vs. hierarchy continues in the industry and is worthy of its own chapter.
Sheet and plate metalwork
Published in Roger Timings, Fabrication and Welding Engineering, 2008
Flattening tools of various forms may be used either in pairs for flattening a returned edge or hem on the edge of sheet metal, or in conjunction with a formed male or female die. Figure 7.11(d) shows a flat male tool (punch) and a formed female tool (die) closing a countersunk seam in a sheet-metal fabrication.
Combining physical shell mapping and reverse-compensation optimisation for spiral machining of free-form surfaces
Published in International Journal of Production Research, 2019
Xiongbing Li, Zhiping Liu, Fulin Wang, Bing Yi, Yongfeng Song
For the machining of free-form surfaces, the surface flattening strategy has a distinct influence on the flattening distortion and path distribution (Wang, Smith, and Yuen 2002). A good surface flattening strategy is helpful in restraining flattening distortion, reducing scallop-height error, and improving the machining efficiency as well as surface quality. Consequently, a novel method is proposed to map the free-form surfaces to a plane based on a physical shell model, hereafter called physical shell mapping. The physical shell model is solved based on stretching energy, bending energy, and global energy. Herein, both local projection and global constraints are taken into account. The basic flow of surface flattening is as follows: To flatten the triangular mesh surface, a physical shell model is built based on the implicit Euler time integration.The spring-mass model is used for locally solving the stretching energy, helping to minimise the side-length difference of triangular facets caused by surface flattening.Local bending potential energy is calculated by employing the hinge model, which results in flattening of surfaces with an isometric distortion.By pre-computing the sparse Cholesky factorisation (Chen et al. 2018), the physical shell model is globally solved. The planar region is acquired after iteratively solving the global energy equation.
Three-dimensional wound flattening method for mapping skin mechanical properties based on finite element method
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2023
Xiaogang Ji, Guangquan Wen, Hao Gong, Rong Sun, Huabin Li
Surface flattening is the process of mapping a spatial surface to a specific plane, which is widely used in sheet metal forming (Liu et al. 2013), clothing design (Chung et al. 2008) and other manufacturing fields. Manning (Manning 1980) used isometric tree theory to expand and cut the vamp in 1980. Since then, many scholars have proposed a variety of complex surface flattening methods. Springborn et al. (2008) proposed a conformal parametric algorithm. In the process of solving the shape of surface flattening, the area deformation before and after surface flattening is quantified and distributed to each vertex of the surface, and a new point is placed at the maximum deformation value to reduce the area deformation. Shin (2011) proposed a plane flattening method for anisotropic materials based on constant strain triangle. By changing the elastic ratio between two material axes, different plane shapes can be obtained. Sheffer et al. (2005) transformed the parametric flattening problem of surface into the minimization problem of objective function by constructing the objective function of mesh angle deformation energy based on conformal maps method. San-Vicente et al. (2012) referred to the soft tissue simulation of nonlinear finite element method and used the spring particle model to simulate the mechanical behavior of soft tissue, which provided a new idea for the surface flattening of material deformation simulation. Yi et al. (2018) proposed a method of using physical shell model to expand triangular mesh surface based on edge spring stretching model and hinge bending model. In order to solve the problems of many iterations and large convergence changes in the process of surface flattening optimization, Zheng et al. (2022) conducted initial correction and deformation analysis on the flattening results according to the average flattening error, established a global geometric deformation energy model and obtained the flattening conditions with the minimum energy. Through iteration, the results of initial flattening are optimized. Wei et al. (2022) proposed a surface flattening algorithm based on local rigid registration and global energy optimization. The experimental results show that the method is stable and reliable. Good surface flattening effect can be obtained under free boundary conditions.