Nonlinear viscoelasticity of strain rate type: an overview

There are some materials in nature that experience deformations that are not elastic. Viscoelastic materials are some of them. We come across many such materials in our daily lives through a number of interesting applications in engineering, material science and medicine. This article concerns itself with modelling of the nonlinear response of a class of viscoelastic solids. In particular, nonlinear viscoelasticity of strain rate type, which can be described by a constitutive relation for the stress function depending not only on the strain but also on the strain rate, is considered. This particular case is not only favourable from a mathematical analysis point of view but also due to experimental observations, knowledge of the strain rate sensitivity of viscoelastic properties is crucial for accurate predictions of the mechanical behaviour of solids in different areas of applications. First, a brief introduction of some basic terminology and preliminaries, including kinematics, material frame-indifference and thermodynamics, is given. Then, considering the governing equations with constitutive relationships between the stress and the strain for the modelling of nonlinear viscoelasticity of strain rate type, the most general model of interest is obtained. Then, the long-term behaviour of solutions is discussed. Finally, some applications of the model are presented.

Vibration response and band gap characteristics of functionally graded frame structure

Vibration response and band gap characteristics of the functionally graded frame structures are investigated based on the first-order shear deformation theory. The material properties of functionally graded material rods vary continuously in thickness direction according to a power law. Spectral stiffness matrix of the periodic functionally graded material frame structure in the global coordinate system is derived in detail. Consequently, the vibration band gap properties of the functionally graded material frame structure can be calculated and analyzed by using the spectral element method. The calculation accuracy for dynamic responses of the functionally graded material frame structure is validated by the finite element method. The results demonstrate that the wider band gaps in the low and medium frequency ranges can be achieved for the functionally graded frame structures comparing with the homogeneous ones. Moreover, the frequency windows and ranges for the band gaps of the functionally graded material frame structure can be effectively adjusted through designing the gradient indexes for the functionally graded material rods, which provide a novel idea for vibration suppression of frame structures.

Modal Reduction Procedures for Flexible Multibody System Applications

The comprehensive simulation of flexible multibody systems calls for the ability to model various types of structural components such as rigid bodies, beams, plates, and kinematic joints. Modal components test offer additional modeling versatility by enabling the treatment of complex, three-dimensional structures via modal reduction procedures based on the small deformation assumption. In this paper, the problem is formulated within the framework of the motion formalism. The kinematic description involves simple, straightforward frame transformations and leads to deformation measures that are both objective and tensorial. Derivatives are expressed in the material frame, which results in the remarkable property that the tangent matrices are independent of the configuration of the modal component with respect to an inertial frame. This implies a reduced level of geometric nonlinearity as compared to standard description. In particular, geometrically nonlinear problems can be solved with the constant tangent matrices of the reference configuration, without re-evaluation and re-factorization.

Finite elasticity

This chapter provides an overview of the theory of finite elasticity including a review of finite deformation kinematic measures, stress tensors for finite deformation, the concept of material frame invariance and change of frame, and constitutive relations. Material symmetry is discussed, and the important case of isotropy is presented. Special considerations needed for incompressible isotropic materials are elaborated upon.

MINIMALISASI BIAYA PENYEDIAAN FRAME SCAFFOLDING DENGAN METODE LINEAR PROGRAMMING PADA PROYEK X

ABSTRACTIn the process of casting, we need a temporary structure that functions as a support or called scaffolding. Scaffolding frame is one type of modern scaffolding that is very commonly used today in high rise building construction. The amount of frame scaffolding needs on a project is not small so the amount of supply of frame scaffolding material can affect cost control on a project. In this study, the linear programming method is used to minimize the cost of providing frame scaffolding material in Project X. The study uses various combinations of frame scaffolding component sizes in casting beams and floor slabs with constraints or problem constraints such as storage of frame scaffolding components, load capacity the maximum that can be held by frame scaffolding, the supply of material quantities, and the casting cycle. By using the linear programming method, a cost savings of 4.3% can be made from the total cost of providing frame scaffolding in Project X if frame scaffolding material is provided with a volume of 3 floors, then 20.23% if frame scaffolding material is provided as much volume 2.5 floor, and 28.7% if frame scaffolding material is provided as much as the minimum floor volume.ABSTRAKDalam proses pengecoran, dibutuhkan struktur sementara yang berfungsi sebagai penyangga atau yang disebut perancah. Saat ini, frame scaffolding merupakan salah satu jenis perancah modern yang sangat umum digunakan pada konstruksi gedung bertingkat. Jumlah kebutuhan frame scaffolding pada suatu proyek tidaklah sedikit sehingga jumlah penyediaan material frame scaffolding ini dapat mempengaruhi pengendalian biaya pada suatu proyek. Pada penelitian ini, digunakan metode linear programming untuk dapat meminimalisasi biaya penyediaan material frame scaffolding pada Proyek X. Penelitian menggunakan berbagai kombinasi ukuran komponen frame scaffolding pada pengecoran balok dan pelat lantai dengan kendala berupa tempat penyimpanan komponen frame scaffolding, kapasitas beban maksimum yang dapat ditahan oleh frame scaffolding, penyediaan jumlah material, dan siklus pengecoran. Dengan menggunakan metode linear programming, dapat dilakukan penghematan biaya sebesar 4,3% dari total biaya penyediaan frame scaffolding pada Proyek X jika material frame scaffolding disediakan sebanyak volume 3 (tiga) lantai, dapat dilakukan penghematan sebesar 20,23% jika material frame scaffolding disediakan sebanyak volume 2,5 (dua setengah lantai), dan sebesar 28,7% jika material frame scaffolding disediakan sebanyak volume lantai yang paling minimal. Selain itu, dengan menggunakan metode linear programming dapat diketahui jumlah material frame scaffolding yang paling baik sesuai dengan kondisi-kondisi di lapangan.

Noll’s Axioms and Formulation of the Closure Relations for the Subgrid Turbulent Tensor in Large Eddy Simulation

In this paper, the relation between the Noll formulation of the principle of material frame indifference and the principle of turbulent frame indifference in large eddy simulation, is revised. The principle of material frame indifference and the principle of turbulent frame indifference proposed by Hutter and Joenk imposes that both constitutive equations and turbulent closure relations must respect both the requirement of form invariance, and the requirement of frame independence. In this paper, a new rule for the formalization of turbulent closure relations, is proposed. The generalized SGS turbulent stress tensor is related exclusively to the generalized SGS turbulent kinetic energy, which is calculated by means of its balance equation, and the modified Leonard tensor.

Studi Kebijakan Pengembangan Kurikulum Pendidikan Agama Islam Model Kurikulum 2013

Curriculum development is a process of activities that produce conceptual, material, frame of mind, and curriculum which are developed through the preparation, implementation, assessment and refinement after completion, so there is a verification stage so that it can be seen as feasible and not a new curriculum candidate as a result of development carried out in the curriculum. This study discusses in depth about the development of curriculum PAI 2013 Curriculum model. This study aims to determine the extent of the study of the development of Islamic education curriculum curriculum curriculum models in 2013. This research uses the literature review method. Data collection was carried out using documentation study techniques. The results of this study are seen in the components of the PAI curriculum which each have correlations and are interrelated as a form of cooperation in the realization of the PAI curriculum so that it remains relevant to the reality, time, community conditions, student conditions, and the development conditions of science and technology. It should be emphasized in the PAI curriculum that is the process of instilling Islamic values ​​as the main axis that is characteristic. Nevertheless educators continue to strive in developing curriculum especially on PAI material so that the PAI learning system remains interesting to answer the challenges of the times and make PAI material as attractive as possible so that students who have critical reasoning and are unusually intelligent are not saturated and autistic. We can see the common thread that one component of the PAI learning system is the PAI curriculum which consists of several components, namely objectives, materials, methods, and evaluation. While the other components of the PAI learning system are educators, students, institution managers, and learning resources besides educators. So the authors propose by adding religious and collaborative values ​​to maximize the PAI curriculum in implementing it in schools.

Constitutive relations for polar continua based on statistical mechanics and spatial averaging

The purpose of the current work is the formulation of macroscopic constitutive relations, and in particular continuum flux densities, for polar continua from the underlying mass point dynamics. To this end, generic microscopic continuum field and balance relations are derived from phase space transport relations for expectation values of point fields related to additive mass point quantities. Given these, microscopic energy, linear momentum and angular momentum, balance relations are obtained in the context of the split of system forces into non-conservative and conservative parts. In addition, divergence–flux relations are formulated for the conservative part of microscopic supply-rate densities. For the case of angular momentum, two such relations are obtained. One of these is force-based, and the other is torque-based. With the help of physical and material theoretic restrictions (e.g. material frame-indifference), reduced forms of the conservative flux densities are obtained. In the last part of the work, formulation of macroscopic constitutive relations from their microscopic counterparts is investigated in the context of different spatial averaging approaches. In particular, these include (weighted) volume-averaging based on a localization function, surface averaging of normal flux densities based on Cauchy flux theory and volume averaging with respect to centre of mass.