Some aspects of redesigning in aluminium

THE development of high strength aluminium alloys has provided a great incentive to many manufacturers to convert their products from other metals to alumi-nium.* In all such applications the specific mechan- ical and physical properties of each structural mate- rial have to be considered in the context of the material and labour costs which directly govern the efficiency and economy of a design : a third indirect guiding factor being the cost of maintenance. One or more of the following characteristics has or have in many cases turned the decision in favour of using aluminium

Ordered Rate Constitutive Theories for Non-Classical Thermofluids Based on Convected Time Derivatives of the Strain and Higher Order Rotation Rate Tensors Using Entropy Inequality

This work is licensed under a Creative Commons Attribution 4.0 International License.This paper considers non-classical continuum theory for thermoviscous fluids without memory incorporating internal rotation rates resulting from the antisymmetric part of the velocity gradient tensor to derive ordered rate constitutive theories for the Cauchy stress and the Cauchy moment tensor based on entropy inequality and representation theorem. Using the generalization of the conjugate pairs in the entropy inequality, the ordered rate constitutive theory for Cauchy stress tensor considers convected time derivatives of the Green’s strain tensor (or Almansi strain tensor) of up to orders nε as its argument tensors and the ordered rate constitutive theory for the Cauchy moment tensor considers convected time derivatives of the symmetric part of the rotation gradient tensor up to orders nΘ . While the convected time derivatives of the strain tensors are well known the convected time derivatives of higher orders of the symmetric part of the rotation gradient tensor need to be derived and are presented in this paper. Complete and general constitutive theories based on integrity using conjugate pairs in the entropy inequality and the generalization of the argument tensors of the constitutive variables and the representation theorem are derived and the material coefficients are established. It is shown that for the type of non-classical thermofluids considered in this paper the dissipation mechanism is an ordered rate mechanism due to convected time derivatives of the strain tensor as well as the convected time derivatives of the symmetric part of the rotation gradient tensor. The derivations of the constitutive theories presented in the paper is basis independent but can be made basis specific depending upon the choice of the specific basis for the constitutive variables and the argument tensors. Simplified linear theories are also presented as subset of the general constitutive theories and are compared with published works

Consistency and Validity of the Mathematical Models and the Solution Methods for BVPs and IVPs Based on Energy Methods and Principle of Virtual Work for Homogeneous Isotropic and Non-Homogeneous Non-Isotropic Solid Continua

Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (I) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (δI) set to zero is a necessary condition for an extremum of I. In this approach one could use δI = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from δI = 0, which is also satisfied by a solution obtained from δI = 0. The Euler’s equations obtained from δI = 0 indeed are the mathematical model associated with the energy functional I. In case of BVPs we follow the same approach except in this case, the energy functional I consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles i.e. conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper

Thermodynamic Consistency of Plate and Shell Mathematical Models in the Context of Classical and Non-Classical Continuum Mechanics and a Thermodynamically Consistent New Thermoelastic Formulation

Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models

Deep Learning for Conversions Between Melodic Frameworks of Indian Classical Music

The CycleGAN deep learning framework has been successfully used for image style transfer in important domains such as medical diagnosis. This paper describes attempts, first of their kind, at using the framework for converting Indian Classical music from one melodic framework, called raga or raag, to another. From the audio samples generated and their visualizations, it is evident that the experiments were reasonably successful in converting music in Hindustani Classical raga to music in Indian Carnatic raga and vice versa. The insights presented in the paper are hoped to inspire further work to revolutionize the use of technology to improvise Indian Classical music

Moxifloxacin (Avelox) Induced Thrombotic Thrombocytopenic Purpura

We report a case of a 66-year-old African-American female who presented with complaints of progressively worsening weakness, shortness of breath on minimal exertion, lethargy for the last few days, and short episodes of aphasia lasting 20–30 seconds. Prior to presentation, she was treated with two courses of moxifloxacin for sinusitis. Laboratory examination was remarkable for anemia and thrombocytopenia with elevated lactate dehydrogenase and no evidence of renal failure. Peripheral smear showed numerous schistocytes and she was diagnosed with thrombotic thrombocytopenic purpura. Moxifloxacin was identified as the offending agent. The patient was treated with prednisone and plasmapheresis. To the best of our knowledge, this is the first reported case of thrombotic thrombocytopenic purpura associated with the use of moxifloxacin. Although rare, physicians should be aware of this serious complication associated with its use

Analisa Performa Steam Jet Ejector Pltp Skala Kecil Pada Kondisi Operasi Berbeda

Telah dilakukan penelitian ejector untuk proses ekstraksi Non Condensable Gas (NCG) dengan menggunakan steam yang bergerak dengan kecepatan tinggi. Pada penelitian ini dilakukan variasi tekanan kondenser untuk mengetahui performa ejector pada kondisi operasi tekanan kondenser yang berbeda. Performa ejector dapat dilihat dari entrainment ratio yang dihasilkan. Hasil penelitian ini menunjukkan bahwa kondisi operasi berbeda akan menghasilkan entrainment ratio yang berbeda. Nilai entrainment ratio menunjukkan kondisi desain ejector dan pada penelitian ini didapatkan kondisi operasi ejector on-design dan off-desig

Error Estimations, Error Computations, and Convergence Rates in FEM for BVPs

This paper presents derivation of a priori error estimates and convergence rates of finite element processes for boundary value problems (BVPs) described by self adjoint, non-self adjoint, and nonlinear differential operators. A posteriori error estimates are discussed in context with local approximations in higher order scalar product spaces. A posteriori error computational framework (without the knowledge of theoretical solution) is presented for all BVPs regardless of the method of approximation employed in constructing the integral form. This enables computations of local errors as well as the global errors in the computed finite element solutions. The two most significant and essential aspects of the research presented in this paper that enable all of the features described above are: 1) ensuring variational consistency of the integral form(s) resulting from the methods of approximation for self adjoint, non-self adjoint, and nonlinear differential operators and 2) choosing local approximations for the elements of a discretization in a subspace of a higher order scalar product space that is minimally conforming, hence ensuring desired global differentiability of the approximations over the discretizations. It is shown that when the theoretical solution of a BVP is analytic, the a priori error estimate (in the asymptotic range, discussed in a later section of the paper) is independent of the method of approximation or the nature of the differential operator provided the resulting integral form is variationally consistent. Thus, the finite element processes utilizing integral forms based on different methods of approximation but resulting in VC integral forms result in the same a priori error estimate and convergence rate. It is shown that a variationally consistent (VC) integral form has best approximation property in some norm, conversely an integral form with best approximation property in some norm is variationally consistent. That is best approximation property of the integral form and the VC of the integral form is equivalent, one cannot exist without the other, hence can be used interchangeably. Dimensional model problems consisting of diffusion equation, convection-diffusion equation, and Burgers equation described by self adjoint, non-self adjoint, and nonlinear differential operators are considered to present extensive numerical studies using Galerkin method with weak form (GM/WF) and least squares process (LSP) to determine computed convergence rates of various error norms and present comparisons with the theoretical convergence rates

A More Complete Thermodynamic Framework For Fluent Continua

Polar decomposition of the changing velocity gradient tensor in a deforming fluent continua into pure stretch rates and rates of rotations shows that a location and its neighboring locations can experience different rates of rotations during evolution. Alternatively, we can also consider decomposition of the velocity gradient tensor into symmetric and skew symmetric tensors. The skew symmetric tensor is also a measure of pure rates of rotations whereas the symmetric tensor is a measure of strain rates. The measures of the internal rates of rotations due to deformation in the two approaches describe the same physics but in different forms. Polar decomposition gives the rate of rotation matrix and not the rates of rotation angles whereas the skew symmetric part of the velocity gradient tensor yields rates of rotation angles that are explicitly defined in terms of velocity gradients. These varying rates of rotations at neighboring locations arise due to varying deformation of the continua, hence are internal to the volume of matter and are explicitly defined by deformation. If the internal varying rates of rotations are resisted by the continua, then there must exist internal moments corresponding to these. The internal rates of rotations and the corresponding moments can result in additional rate of energy storage or rate of dissipation. This physics is all internal to the deforming continua and exists in all deforming isotropic, homogeneous fluent continua but is completely neglected in the presently used thermodynamic framework for fluent continua. In this paper we present derivation of a more complete thermodynamic framework in which the derivation of the conservation and balance laws consider additional physics due to varying rates of rotations. The currently used thermodynamic framework for fluent continua is a subset of the thermodynamic framework presented in this paper. The continuum theory presented here considers internal varying rates of rotations and the associated conjugate moments in the derivation of conservation and balance laws, thus the theory presented in this paper can be called “a polar continuum theory” but is different than micropolar continuum theories published currently in which material points have six external degrees of freedom i.e. the rotation rates are additional external degrees of freedom. In the remainder of the paper we refer to this new thermodynamic framework as ‘a polar continuum theory’. The continuum theory presented here only accounts for internal rotation rates and associated moments that exist as a consequence of deformation but are neglected in the present theories hence this theory results in a more complete thermodynamic framework. The polar continuum theory and the resulting thermodynamic framework presented in this paper is suitable for compressible as well as incompressible thermoviscous fluent continua such as Newtonian, Power law, Carreau-Yasuda fluids etc. and thermoviscoelastic fluent continua such as Maxwell, Oldroyd-B, Giesekus etc. The thermodynamic framework presented here is applicable to all isotropic, homogeneous fluent continua. Obviously the constitutive theories will vary depending upon the choice of physics. These are considered in subsequent papers