A Genetically Based Combination of Visual Saliency and Roughness for FR 3D Mesh Quality Assessment: A Statistical Study

In this paper, we present a full-reference quality assessment metric based on the information of visual saliency. The saliency information is provided under the form of degrees associated to each vertex of the surface mesh. From these degrees, statistical attributes reflecting the structures of the reference and distorted meshes are computed. These are used by four comparisons functions genetically optimized that quantify the structure differences between a reference and a distorted mesh. We also present a statistical comparison study of six full-reference quality assessment metrics for 3D meshes. We compare the objective metrics results with humans subjective scores of quality considering the 3D meshes in one hand and the distorsion types in the other hand. Also, we show which metrics are statistically superior to their counterparts. For these comparisons we use the Spearman Rank Ordered Correlation Coefficient and the hypothetic test of Student (ttest). To attest the pertinence of the proposed approach, a comparison with a ground truth saliency and an application associated to the assessment of the visual rendering of smoothing algorithms are presented. Experimental results show that the proposed metric is very competitive with the state-of-the-art.

Convergence improvement of the simultaneous relaxation method used in the finite element analysis of incompressible fluid flows

Purpose This paper aims to present an improved finite element method used for achieving faster convergence in simulations of incompressible fluid flows. For stable computations of incompressible fluid flows, it is important to ensure that the flow field satisfies the equation of continuity in each element of a generally distorted mesh. The study aims to develop a numerical approach that satisfies this requirement based on the highly simplified marker-and-cell (HSMAC) method and increases computational speed by introducing a new algorithm into the simultaneous relaxation of velocity and pressure. Design/methodology/approach First, the paper shows that the classical HSMAC method is equivalent to a Jacobi-type method in terms of the simultaneous relaxation of velocity and pressure. Then, a Gauss–Seidel or successive over-relaxation (SOR)-type method is introduced in the Newton–Raphson iterations to take into account all the derivative terms in the first-order Taylor series expansion of a nodal-averaged error explicitly. Here, the nine-node quadrilateral (Q2–Q1) elements are used. Findings The new finite element approach based on the improved HSMAC algorithm is tested on fluid flow problems including the lid-driven square cavity flow and the flow past a circular cylinder. The results show significant improvement of the convergence property with the accuracy of the numerical solutions kept unchanged even on a highly distorted mesh. Originality/value To the best of the author’s knowledge, the idea of using the Gauss–Seidel or SOR method in the simultaneous relaxation procedure of the HSMAC method has not been proposed elsewhere.

On the accuracy and convergence of the hybrid FE-meshfree Q4-CNS element in surface fitting problems

In the last decade, several hybrid methods combining the finite element and meshfree methods have been proposed for solving elasticity problems. Among these methods, a novel quadrilateral four-node element with continuous nodal stress (Q4-CNS) is of our interest. In this method, the shape functions are constructed using the combination of the ‘non-conforming’ shape functions for the Kirchhoff’s plate rectangular element and the shape functions obtained using an orthonormalized and constrained least-squares method. The key advantage of the Q4-CNS element is that it provides the continuity of the gradients at the element nodes so that the global gradient fields are smooth and highly accurate. This paper presents a numerical study on the accuracy and convergence of the Q4-CNS interpolation and its gradients in surface fitting problems. Several functions of two variables were employed to examine the accuracy and convergence. Furthermore, the consistency property of the Q4-CNS interpolation was also examined. The results show that the Q4-CNS interpolation possess a bi-linier order of consistency even in a distorted mesh. The Q4-CNS gives highly accurate surface fittings and possess excellent convergence characteristics. The accuracy and convergence rates are better than those of the standard Q4 element.

8-node and 12-node plane elements based on assumed stress quasi-conforming method immune to distorted mesh

Purpose Severe accuracy loss may occur when finite element comes to the distorted mesh model, and the calculation may fail when element mesh degenerates into concave quadrangle or the element boundary is curved. This is a valuable research topic, and many efforts have been made to develop new finite element models. This paper aims to propose two quasi-conforming membrane elements based on the assumed stress quasi-conforming method and fundamental analytical solutions to overcome the difficulties. Design/methodology/approach First, the fundamental analytical solutions which satisfied both the equilibrium and the compatibility relations of plane stress problem are used as the initial assumed stress of both elements. Then, the stress-function matrices are used as the weighted functions to weaken the strain-displacement equations, which makes only string-net functions on the boundary of the elements are needed in the process of strain integration. Finally, boundary interpolation functions expressed by unknown nodal displacement parameters are adopted to the process of strain integration. Findings The formulations of both elements are simple and concise, and the elements are immune to the distorted mesh, which can be used to the mesh shape degenerates into a triangle or concave quadrangle and curved-side element. The results of the numerical tests have proven that the new models possess high accuracy. Originality/value New formulations of quasi-conforming method are described is detail, and the new strategy exhibits advantages of both analytical and discrete methods.

A Smoothed Finite Element-Based Elasticity Model for Soft Bodies

One of the major challenges in mesh-based deformation simulation in computer graphics is to deal with mesh distortion. In this paper, we present a novel mesh-insensitive and softer method for simulating deformable solid bodies under the assumptions of linear elastic mechanics. A face-based strain smoothing method is adopted to alleviate mesh distortion instead of the traditional spatial adaptive smoothing method. Then, we propose a way to combine the strain smoothing method and the corotational method. With this approach, the amplitude and frequency of transient displacements are slightly affected by the distorted mesh. Realistic simulation results are generated under large rotation using a linear elasticity model without adding significant complexity or computational cost to the standard corotational FEM. Meanwhile, softening effect is a by-product of our method.

Accurate Prediction Approach of 3D Trimming Line for Auto Panel Part

It is difficult to obtain 3D trimming line using traditional prediction methods for auto panel parts. An initial geometrical development method with element layer is proposed based on one step inverse analysis theory for this problem. The flange mesh can be unfold onto the die surface layer by layer according to nodal adjacent element relation, then the above development mesh is smoothed by mesh smoothing method with sliding constraint surface in order to delete overlap and distorted mesh, the 3D initial mesh can be obtained for one step inverse analysis method. The accurate 3D trimming line of auto panel part can be achieved by plasticity iteration of one step inverse analysis. A typical real part of 3D trimming line prediction is selected to prove this method, the comparison results between the simulated and experimental values show that this method has enough precision and can handle complex parts, satisfies the engineering practical demands.