A Generalisation of the hill's quadratic yield function for planar plastic anisotropy to consider loading direction

In this work, a new generalised quadratic yield function for plane stress analysis that is able to describe the plastic anisotropy of metals and also the asymmetric behaviour in tension-compression typical of the Hexagonal Closed-Pack (HCP) materials, is developed. The new yield function has a quadratic form in the stress tensor and it simultaneously predicts the r-values and directional flow stresses, which is shown to agree very well with exper- imental results. It also accurately describes the biaxial symmetric stress state which is fundamental for the accurate modelling of aluminium alloys. The new quadratic yield function represents the non-symmetric biaxial stress state by performing a linear interpolation from pure uniaxial loading to a bi- axial symmetric stress state. The main advantages of this new yield function is that it can be used for the modelling of metals with any crystallographic structure (BCC, FCC or HCP), it only has ve anisotropic coeffcients and also that it is a simple quadratic yield criterion that is able to accurately reproduce the plastic anisotropy of metals whilst using an associated flow rule

On Contact Modelling in IsoGeometric Analysis

IsoGeometric Analysis (IGA) has proved to be a reliable numerical tool for the simulation of structural behaviour and uid mechanics. The main reasons for this popularity are essentially due to: i) the possibility of using higher order polynomials for the basis functions; ii) the high convergence rates possible to achieve; iii) the possibility to operate directly on CAD geometry without the need to resort to a mesh of elements. The major drawback of IGA is the non-interpolatory characteristic of the basis functions, which adds a di culty in handling essential boundary conditions and make it particularly challenging for contact analysis. In this work, the IGA is expanded to include frictionless contact procedures for sheet metal forming analyses. Non-Uniform Rational B-Splines (NURBS) are going to be used for the modelling of rigid tools as well as for the modelling of the deformable blank sheet. The contact methods developed are based on a two-step contact search scheme, where during the rst step a global search algorithm is used for the allocation of contact knots into potential contact faces and a second (local) contact search scheme where point inversion techniques are used for the calculation of the contact penetration gap. For completeness, elasto-plastic procedures are also included for a proper description of the entire IGA of sheet metal forming processes

A unified dynamic similitude model for solid continuum

Copyright © 2022 The Authors. Dynamic similitude has proven to be a valuable tool, which is widely adopted in fluid mechanics. However, even with the ever-growing interest in dynamic similitude in solid mechanics, there is still no unified scaling law applicable to any given solid structure or system, and this has prevented the broad adoption of similitude in the field. Here we develop a unified similitude model for solid mechanics using the momentum and the energy conservation. The model allows for the use of different materials in both elastic and plastic regimes. Never reported dimensionless numbers are derived for the first time in this article, and this set of numbers is sufficient for strictly accurate dynamic similitude of any solid structure. Very different case studies are considered, and the perfect agreement seen in compared results confirms the accuracy of the developed scaling model. The exactness of the dimensionless numbers is also confirmed through analytical solutions. The model allows for the scaling of strain rate and, for the first time, the scaling of the strain state between the full-scale structure and its scaled replica

A Unified Dynamic Similitude of Solid Continuum and its Application in Aeroelastic Structures

Copyright © 2022 The Authors. The use of dynamic similitude has been widely proven in fluid mechanics. With the drive for efficient aircraft wing through high aspect ratio wings comes the growing need for much more accurate aeroelastic analyses of aircraft wings and more accurate scaled experimental tests. Even with this need for dynamic similitude in solid mechanics, there is still no unified exact scaling law applicable to any given solid structure or system. Here we present a recently proposed unified similitude model for solid mechanics using the momentum and the energy conservation. The model allows for the use of different materials in both elastic and plastic regimes. Never reported dimensionless numbers are derived for the first time in this article, and this set of numbers is sufficient for strictly accurate dynamic similitude of any solid structure. The application of the unified model is demonstrated for the first time in an aeroelastic structure and in aerospace structures through case studies. The very good agreement seen in compared results confirms the accuracy of the developed scaling model and the exactness of the dimensionless numbers

The thermal analysis of cutting/grinding processes by meshless finite block method

© 2018 Elsevier Ltd Development of the Finite Block Method (FBM) is presented, with the introduction of infinite elements for the first time, for predicting stationary and transient heat conduction in cutting/grinding processes. Utilizing the Lagrange series the first order partial differential matrix is derived, adopting a mapping technique, followed by the construction of the higher order derivative matrix. For linear stationary heat conductivity three free parameters including the velocity of the workpiece, the cooling coefficient and the inclined angle of the contact zone, together with their effects on temperature, are observed. For the transient heat conduction study, the Laplace transformation method and Durbin's inverse technique are employed. Numerical solutions are discussed and comparisons made with the finite element method and analytical solutions, demonstrating the accuracy and convergence of the finite block method

Numerical Investigation into the Effects of Turbulence Modelling on the Aeroelastic Analysis of Flexible Wings

Copyright © 2022 The Authors. As wings are becoming more flexible, existing aeroelastic analysis methods may struggle to accurately resolve the complex flow around oscillating wings. A numerical case study is performed to compare the aeroelastic predictions obtained for a wing with two degrees of freedom when turbulence models of varying fidelity are used. Results are presented and compared in the time and frequency domain for simulations using Reynolds Averaged Navier Stokes and Detached Eddy turbulence models. These results show significant differences be- tween the results obtained, particularly in the time domain. The numerical methodology, setup and results for this case study are presented in this paper

STABILITY LOBES PREDICTION FOR CORNER RADIUS END MILL USING NONLINEAR CUTTING FORCE COEFFICIENTS

There are a vast number of different types of end mill tools used in the manufacturing industry, each type with a unique shape. These tool shapes have a direct influence on the cutting force it generates during machining. This article presents a more accurate approach to predicting the stability margin in machining by considering the cutting force coefficients and axial immersion angle as variables along the axial depth of cut. A numerical approach to obtaining a converged solution to the stability model is presented. The results obtained are validated using experimental results and a very good agreement is seen.Engineering and Physical Sciences Research Counci

Dynamic large deformation analysis of a cantilever beam

National Natural Science Foundation of Chin

A new damping modelling approach and its application in thin wall machining

In this paper, a new approach to modelling the damping parameters and its application in thin wall machining is presented. The approach to predicting the damping parameters proposed in this paper eliminates the need for experiments otherwise used to acquire these parameters. The damping model proposed was compared with available damping models and experimental results. A finite element analysis and Fourier transform approach has been used to obtain frequency response function (FRF) needed for stability lobes prediction. Several predicted stable regions using both experimental and numerical FRF’s for various examples gave a good comparison.Engineering and Physical Sciences Research Counci