On the use of elemental quantities to compute NSIFs at pointed V-notches with non-regular coarse meshes

2021 ◽  
pp. 103083
Author(s):  
Michele Zappalorto ◽  
Alessandro Pontefisso ◽  
Paolo Andrea Carraro
Keyword(s):  
Coarse Meshes

scholarly journals The Role of Mesh Generation, Adaptation, and Refinement on the Computation of Flows Featuring Strong Shocks

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Aldo Bonfiglioli ◽  
Renato Paciorri ◽  
Andrea Di Mascio
Keyword(s):  
Shock Waves ◽  
Mesh Generation ◽  
The Other ◽  
Shock Capturing ◽  
Structured Grids ◽  
Computational Mesh ◽  
Versatile Technique ◽  
Coarse Meshes ◽  
Shock Fitting

Within a continuum framework, flows featuring shock waves can be modelled by means of either shock capturing or shock fitting. Shock-capturing codes are algorithmically simple, but are plagued by a number of numerical troubles, particularly evident when shocks are strong and the grids unstructured. On the other hand, shock-fitting algorithms on structured grids allow to accurately compute solutions on coarse meshes, but tend to be algorithmically complex. We show how recent advances in computational mesh generation allow to relieve some of the difficulties encountered by shock capturing and contribute towards making shock fitting on unstructured meshes a versatile technique.

scholarly journals Exact geometry solid-shell element based on a sampling surfaces technique for 3D stress analysis of doubly-curved composite shells

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
G. M. Kulikov ◽  
A. A. Mamontov ◽  
S. V. Plotnikova ◽  
S. A. Mamontov
Keyword(s):  
Stress Analysis ◽  
Numerical Solutions ◽  
Variational Equation ◽  
Shell Element ◽  
Middle Surface ◽  
Superior Performance ◽  
Lagrange Polynomials ◽  
Shell Formulation ◽  
Coarse Meshes ◽  
Doubly Curved

AbstractA hybrid-mixed ANS four-node shell element by using the sampling surfaces (SaS) technique is developed. The SaS formulation is based on choosing inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell in order to introduce the displacements of these surfaces as basic shell variables. Such choice of unknowns with the consequent use of Lagrange polynomials of degree In − 1 in the thickness direction for each layer permits the presentation of the layered shell formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that allows one to minimize uniformly the error due to the Lagrange interpolation. To implement the efficient analytical integration throughout the element, the enhanced ANS method is employed. The proposed hybrid-mixed four-node shell element is based on the Hu-Washizu variational equation and exhibits a superior performance in the case of coarse meshes. It could be useful for the 3D stress analysis of thick and thin doubly-curved shells since the SaS formulation gives the possibility to obtain numerical solutions with a prescribed accuracy, which asymptotically approach the exact solutions of elasticity as the number of SaS tends to infinity.

scholarly journals Comparison of Efficient Explicit Schemes for Shallow-Water Equations—Characteristics-Based Fractional-Step Method and Multimoment Eulerian Scheme

2007 ◽  
Vol 46 (3) ◽  
pp. 388-395 ◽  
Author(s):  
Yohsuke Imai ◽  
Takayuki Aoki ◽  
Magdi Shoucri
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Parallel Architecture ◽  
Fractional Step ◽  
Processing Unit ◽  
Step Method ◽  
Fractional Step Method ◽  
Central Processing ◽  
Explicit Schemes ◽  
Coarse Meshes

Abstract Two explicit schemes for the numerical solution of the shallow-water equations are examined. The directional-splitting fractional-step method permits relatively large time steps without an iterative process by using a treatment based on the characteristics of the governing equations. The interpolated differential operator (IDO) scheme has fourth-order accuracy in time and space by using a Hermite interpolation function covering local domains, and accurate results are obtained with coarse meshes. It is shown that the two schemes are very efficient for hydrostatic meteorological models from the viewpoints of numerical accuracy and central processing unit time, and the fact that they are explicit makes them suitable for computers with parallel architecture.

scholarly journals Two‐Grid hp ‐DGFEMs on Agglomerated Coarse Meshes

PAMM ◽  
2019 ◽  
Vol 19 (1) ◽  
Author(s):  
Scott Congreve ◽  
Paul Houston
Keyword(s):  
Coarse Meshes

Development of the Cell-based Smoothed Discrete Shear Gap Plate Element (CS-FEM-DSG3) using Three-Node Triangles

2015 ◽  
Vol 12 (04) ◽  
pp. 1540015 ◽  
Author(s):  
T. Nguyen-Thoi ◽  
M. H. Nguyen-Thoi ◽  
T. Vo-Duy ◽  
N. Nguyen-Minh
Keyword(s):  
Static Analysis ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Functionally Graded ◽  
Triangular Element ◽  
Plate Element ◽  
Strain Smoothing ◽  
Discrete Shear Gap ◽  
Transverse Shear Locking ◽  
Coarse Meshes

The paper presents the formulation and recent development of the cell-based smoothed discrete shear gap plate element (CS-FEM-DSG3) using three-node triangles. In the CS-FEM-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the original plate element DSG3 is used to compute the strains and to avoid the transverse shear locking. Then the cell-based strain smoothing technique (CS-FEM) is used to smooth the strains on these three sub-triangles. The numerical examples illustrate four superior properties of the CS-FEM-DSG3 including: (1) being a strong competitor to many existing three-node triangular plate elements in the static analysis; (2) giving high accurate solutions for problems with skew geometries in the static analysis; (3) giving high accurate solutions in free vibration analysis; (4) providing accurate values of high frequencies of plates by using only coarse meshes. Due to its superior and simple properties, the CS-FEM-DSG3 has been now developed for various analyses such as: flat shells, stiffened plates, functionally graded plates, composite plates, piezoelectricity composite plates, cracked plate and plates resting on the viscoelastic foundation subjected to moving loads, etc.

Fatigue Design of Welded Joints by Local Approaches: Comparison between Fictitious Notch Rounding and Strain Energy Averaging

2007 ◽  
Vol 348-349 ◽  
pp. 449-452 ◽  
Author(s):  
Paolo Lazzarin ◽  
Filippo Berto ◽  
D. Radaj
Keyword(s):  
Welded Joints ◽  
Strain Energy ◽  
Control Volume ◽  
Local Strain ◽  
Stress Distributions ◽  
Good Correspondence ◽  
Load Carrying ◽  
Weld Toe ◽  
Weld Root ◽  
Coarse Meshes

The paper demonstrates the close correspondence between two local approaches to assess the fatigue strength of welded joints: Radaj’s approach based on fictitious notch rounding and a recently proposed approach based on the local strain energy density (SED) averaged over a given control volume. This volume surrounds the weld root or weld toe, both modelled as sharp (zero radius) V-notches with different opening angles. The two approaches are applied to load carrying and non-load carrying cruciform joints and the theoretical fatigue notch factors Kf are compared. The SED averaged over the control volume is determined from finite element models with very fine meshes, as typically designed to evaluate the intensity of the asymptotic stress distributions, and also from coarse meshes, showing a surprisingly good correspondence.

High Order Well-Balanced Weighted Compact Nonlinear Schemes for the Gas Dynamic Equations under Gravitational Fields

2017 ◽  
Vol 7 (4) ◽  
pp. 697-713
Author(s):  
Zhen Gao ◽  
Guanghui Hu
Keyword(s):  
Steady State Solution ◽  
High Order ◽  
Dynamic Equations ◽  
High Order Accuracy ◽  
Local Characteristic ◽  
Gravitational Fields ◽  
Strong Discontinuities ◽  
Gas Dynamic ◽  
Coarse Meshes ◽  
Gas Dynamic Equations

AbstractIn this study, we propose a high order well-balanced weighted compact nonlinear (WCN) scheme for the gas dynamic equations under gravitational fields. The proposed scheme is an extension of the high order WCN schemes developed in (S. Zhang, S. Jiang, C.-W Shu, J. Comput. Phys. 227 (2008) 7294-7321). For the purpose of maintaining the exact steady state solution, the well-balanced technique in (Y. Xing, C.-W Shu, J. Sci. Comput. 54 (2013) 645-662) is employed to split the source term into two terms. The proposed scheme can maintain the isothermal equilibrium solution exactly, genuine high order accuracy and resolve small perturbations of the hydrostatic balance state on the coarse meshes. Furthermore, in order to capture the strong discontinuities and large gradients, the fifth-order upwind weighted nonlinear interpolations together with the fourth/sixth order cell-centered compact schemes with local characteristic projections are used to construct different WCN schemes. Several representative one- and two-dimensional examples are simulated to demonstrate the good performance of the proposed schemes.

The Generalized Conforming Element (GCE) — Theory and Applications

1997 ◽  
Vol 1 (1) ◽  
pp. 63-70 ◽  
Author(s):  
Yuqiu Long ◽  
Zhifei Long ◽  
Yin Xu
Keyword(s):  
Weighted Residual Method ◽  
Energy Principle ◽  
Structural Problems ◽  
Combined Application ◽  
Plate And Shell ◽  
Continuous Problems ◽  
Refined Meshes ◽  
Generalized Conforming Element ◽  
Coarse Meshes ◽  
Limiting Case

The concept of generalized conforming elements and their applications to membrane, plate and shell problems are introduced in this paper. The generalized conforming element method proposed by the first author in 1987 provides a simple and efficient means to deal with structural problems, especially the C1 continuous problems. In the first part of this paper, the theoretical basis of GCE is presented. GCE is a limiting-conforming element which is non-conforming in coarse meshes but tends to be conforming in the limiting case of refined meshes. It is formulated based on the modified potential energy principle and the concept of generalized compatibility conditions. It is a new way to construct the finite elements — combined application of the energy method and the weighted residual method. In the second part of this paper, various models of GCE are illustrated. A series of generalized conforming elements with excellent performance have been constructed, that is, thin and thick plate bending GCE, membrane GCE with drilling freedoms and thin shell GCE.

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