A Validated Analytical Solution for the Two-Dimensional Bending of Aluminium Plates under Creep-Ageing Conditions

2014 ◽  
Vol 622-623 ◽  
pp. 1107-1116 ◽  
Author(s):  
Aaron C. Lam ◽  
Jian Guo Lin
Keyword(s):  
Integration Method ◽  
Ageing Time ◽  
Two Dimensional ◽  
Thickness Strain ◽  
Mechanics Model ◽  
Creep Region ◽  
Two Parameters ◽  
Doubly Curved ◽  
Creep Age Forming ◽  
Good Agreement

An analytical method suitable for modelling the creep-age forming (CAF) of doubly curved aluminium plates is presented. This new mechanics model combines an efficient numerical integration method with a robust set of CAF constitutive equations that has been experimentally validated with AA7055 at a CAF condition. Corresponding finite element simulations show good agreement with the analytical results. Using the validated analytical model to investigate a three-stage CAF process (loading, creep-ageing, and unloading), through-thickness strain distributions are studied for aluminium plates that have been subjected to different creep-ageing time. A creep activation point (CAP) is revealed and a correlation is found between the two parameters introduced in this work – the normalised location of CAP, zCAP and normalised bend ratio, β. More specifically, a linear relationship is found between β and zCAP, which indicates that the onset of creep strain, and hence the sizes of the pure elastic core and the outer creep region, can be readily predictable within the limits of study. It is now possible to simulate two-dimensional bending CAF processes for aluminium alloys that have non-spherical precipitates.

scholarly journals A space structural mechanics model of silicene

2020 ◽  
Vol 234 (1-2) ◽  
pp. 3-10
Author(s):  
Mohsen Motamedi
Keyword(s):  
Natural Frequencies ◽  
Strain Curve ◽  
Structural Mechanics ◽  
Dynamics Simulation ◽  
Mode Shapes ◽  
Two Dimensional ◽  
Stress Strain Curve ◽  
Beam Elements ◽  
Mechanics Model ◽  
Good Agreement

The two-dimensional nanostructures such as graphene, silicene, germanene, and stanene have attracted a lot of attention in recent years. Many studies have been done on graphene, but other two-dimensional structures have not yet been studied extensively. In this work, a molecular dynamics simulation of silicene was done and stress–strain curve of silicene was obtained. Then, the mechanical properties of silicene were investigated using the proposed structural molecular mechanics method. First, using the relations governing the force field and the Lifson–Wershel potential function and structural mechanics relations, the coefficients for the BEAM elements was determined, and a structural mechanics model for silicene was proposed. Then, a silicene sheet with 65 Å × 65 Å was modeled, and Young’s modulus of silicene was obtained. In addition, the natural frequencies and mode shapes of silicene were calculated using finite element method. The results are in good agreement with reports by other papers.

scholarly journals Static and Dynamic Characteristics of Composite Conoidal Shell Roofs

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Kaustav Bakshi ◽  
Dipankar Chakravorty
Keyword(s):  
Boundary Conditions ◽  
Forced Vibration ◽  
Integration Method ◽  
Time Integration ◽  
Laminated Composite ◽  
Time Integration Method ◽  
First Approximation ◽  
Curved Elements ◽  
Doubly Curved ◽  
Good Agreement

A thorough review of the existing literature reflects that forced vibration studies of laminated composite conoidal shells with complicated boundary conditions are missing. Hence, the present paper aims to fill the lacuna. A finite element code utilizing eight-noded doubly curved elements together with modified Sanders’ first approximation theory for thin shells is used to study the forced vibration behavior of moderately thin laminated composite conoidal shells subjected to three different uniformly distributed time-dependent forces. Newmark’s direct time integration method is used to solve the dynamic problem. Results obtained using the present code are compared with the values available in the literature, and a good agreement of the results confirms the accuracy of the proposed code. The transient responses of the laminated shell are studied meticulously for parametric variations like boundary conditions and stacking orders of cross and angle-ply laminates and are compared with bending responses of the shell to conclude on the necessity of the dynamic study.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

scholarly journals Precise Integration Method for Solving Noncooperative LQ Differential Game

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Hai-Jun Peng ◽  
Sheng Zhang ◽  
Zhi-Gang Wu ◽  
Biao-Song Chen
Keyword(s):  
Differential Equation ◽  
Differential Game ◽  
Integration Method ◽  
Transformation Method ◽  
Linear Quadratic ◽  
Riccati Differential Equation ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Direct Integration Method ◽  
Two Parameters

The key of solving the noncooperative linear quadratic (LQ) differential game is to solve the coupled matrix Riccati differential equation. The precise integration method based on the adaptive choosing of the two parameters is expanded from the traditional symmetric Riccati differential equation to the coupled asymmetric Riccati differential equation in this paper. The proposed expanded precise integration method can overcome the difficulty of the singularity point and the ill-conditioned matrix in the solving of coupled asymmetric Riccati differential equation. The numerical examples show that the expanded precise integration method gives more stable and accurate numerical results than the “direct integration method” and the “linear transformation method”.

On Wall Effects in Cavity Flows

1984 ◽  
Vol 28 (01) ◽  
pp. 70-75
Author(s):  
C. C. Hsu
Keyword(s):  
Numerical Results ◽  
Cavity Flows ◽  
Two Dimensional ◽  
Wall Effects ◽  
Free Jet ◽  
Theoretical Predictions ◽  
Experimental Findings ◽  
Good Agreement

Simple wall correction rules for two-dimensional and nearly two-dimensional cavity flows in closed or free jet water tunnels, based on existing linearized analyses, are made. Numerical results calculated from these expressions are compared with existing experimental findings. The present theoretical predictions are, in general, in good agreement with data.

SYMMETRY IN TWO-DIMENSIONAL GRAVITY

1991 ◽  
Vol 06 (13) ◽  
pp. 2331-2346 ◽  
Author(s):  
KAI-WEN XU ◽  
CHUAN-JIE ZHU
Keyword(s):  
Light Cone ◽  
Integration Method ◽  
Symmetry Algebra ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Simple Interpretation ◽  
Brst Charge ◽  
Dimensional Gravity ◽  
Covariant Gauge ◽  
Liouville Action

We study the symmetry of two-dimensional gravity by choosing a generic gauge. A local action is derived which reduces to either the Liouville action or the Polyakov one by reducing to the conformal or light-cone gauge respectively. The theory is also solved classically. We show that an SL (2, R) covariant gauge can be chosen so that the two-dimensional gravity has a manifest Virasoro and the sl (2, R)-current symmetry discovered by Polyakov. The symmetry algebra of the light-cone gauge is shown to be isomorphic to the Beltrami algebra. By using the contour integration method we construct the BRST charge QB corresponding to this algebra following the Fradkin-Vilkovisky procedure and prove that the nilpotence of QB requires c=28 and α0=1. We give a simple interpretation of these conditions.

Free Vibration of Curvilinearly Stiffened Shallow Shells

2013 ◽  
Author(s):  
Peng Shi ◽  
Rakesh K. Kapania
Keyword(s):  
Free Vibration ◽  
Ritz Method ◽  
Beam Theory ◽  
Fe Method ◽  
Shallow Shells ◽  
First Order ◽  
Stiffened Shells ◽  
Method Base ◽  
Doubly Curved ◽  
Good Agreement

The free vibration of curvilinearly stiffened doubly curved shallow shells is investigated by the Ritz method. Base on the first order shear deformation shell theory and Timoshenko’s 3-D curved beam theory, the strain and kinetic energies of the stiffened shells are introduced. Numerical results with different geometrical shells and boundary conditions, and different stiffener locations and curvatures are analyzed to verify the feasibility of the presented Ritz method for solving the problems. The results show good agreement with those using the FE method.

scholarly journals Comparison of GPM Core Observatory and Ground-Based Radar Retrieval of Mass-Weighted Mean Raindrop Diameter at Midlatitude

2018 ◽  
Vol 19 (10) ◽  
pp. 1583-1598 ◽  
Author(s):  
Leo Pio D’Adderio ◽  
Gianfranco Vulpiani ◽  
Federico Porcù ◽  
Ali Tokay ◽  
Robert Meneghini
Keyword(s):  
High Sensitivity ◽  
Sensitivity Study ◽  
Three Dimensions ◽  
Convective Precipitation ◽  
Precipitation Pattern ◽  
Dual Frequency ◽  
Weighted Mean ◽  
Raindrop Size Distribution ◽  
Two Parameters ◽  
Good Agreement

Abstract One of the main goals of the National Aeronautics and Space Administration (NASA) Global Precipitation Measurement (GPM) mission is to retrieve parameters of the raindrop size distribution (DSD) globally. As a standard product of the Dual-Frequency Precipitation Radar (DPR) on board the GPM Core Observatory satellite, the mass-weighted mean diameter Dm and the normalized intercept parameter Nw are estimated in three dimensions at the resolution of the radar. These are two parameters of the three-parameter gamma model DSD adopted by the GPM algorithms. This study investigates the accuracy of the Dm retrieval through a comparative study of C-band ground radars (GRs) and GPM products over Italy. The reliability of the ground reference is tested by using two different approaches to estimate Dm. The results show good agreement between the ground-based and spaceborne-derived Dm, with an absolute bias being generally lower than 0.5 mm over land in stratiform precipitation for the DPR algorithm and the combined DPR–GMI algorithm. For the DPR–GMI algorithm, the good agreement extends to convective precipitation as well. Estimates of Dm from the DPR high-sensitivity (HS) Ka-band data show slightly worse results. A sensitivity study indicates that the accuracy of the Dm estimation is independent of the height above surface (not shown) and the distance from the ground radar. On the other hand, a nonuniform precipitation pattern (interpreted both as high variability and as a patchy spatial distribution) within the DPR footprint is usually associated with a significant error in the DPR-derived estimate of Dm.

Comparison of Numerical and Perturbation Solutions of Two-Dimensional Nonlinear Water-Wave Problems

1976 ◽  
Vol 20 (03) ◽  
pp. 160-170
Author(s):  
Nils Salvesen ◽  
C. von Kerczek
Keyword(s):  
Perturbation Theory ◽  
Numerical Solutions ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Wave System ◽  
Two Dimensional ◽  
Third Order ◽  
Flow Past ◽  
Wave Problems ◽  
Good Agreement

Numerical solutions of the nonlinear problem of the steady two-dimensional potential flow past a submerged line vortex are obtained using the finite-difference iterative technique previously presented by the authors. These solutions are compared in detail with third-order perturbation theory solutions. It is found that very good agreement is obtained for cases of positive circulation of the vortex with strength large enough to produce downstream waves whose steepness is within 15 percent of the maximum possible steepness of irrotational free waves. These computed waves are as steep as the steepest waves obtained in a certain experiment involving the flow past a two-dimensional hydrofoil. For negative circulation, there is substantial difference between the numerical results and third-order perturbation theory. The failure of the perturbation theory is discussed. Details of the far-downstream wave system obtained by the numerical method are compared with other numerical solutions and very high-order perturbation theory solutions of the free-wave problem. Very good agreement is obtained in most cases.

A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

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