• Steel and Composite Structures
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• v.51 no.3
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• pp.261-270
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• 2024

This paper proposes an effective method for optimizing the structure of functionally graded isotropic and incompressible linear elastic materials. The main emphasis is on utilizing a specialized polytopal composite finite element (PCE) technique capable of handling a broad range of materials, addressing common volumetric locking issues found in nearly incompressible substances. Additionally, it employs a continuum model for bi-directional functionally graded (BFG) material properties, amalgamating these aspects into a unified property function. This study thus provides an innovative approach that tackles diverse material challenges, accommodating various elemental shapes like triangles, quadrilaterals, and polygons across compressible and nearly incompressible material properties. The paper thoroughly details the mathematical formulations for optimizing the topology of BFG structures with various materials. Finally, it showcases the effectiveness and efficiency of the proposed method through numerous numerical examples.

• Journal of the Architectural Institute of Korea Structure & Construction
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• v.35 no.9
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• pp.159-169
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• 2019

This work presents the three-dimensional extended strain smoothing approach in the framework of finite element method, so-called smoothed finite element method (S-FEM) for quasi-incompressible hyperelastic materials undergoing the large deformations. The proposed method is known that the incompressible limits, such as over-estimation of stiffness and distorted mesh sensitivity, can be overcome in two dimensions. Therefore, in this paper, the idea of Cell-based, Edge-based and Node-based strain smoothing approaches is extended to three-dimensions. The construction of subcells and smoothing domains for each methods are explained. The smoothed strain-displacement matrix and the stiffness matrix are obtained on each smoothing domain in the same manner with two-dimensional S-FEM. Various numerical tests are studied to demonstrate the validity and accuracy of 3D-S-FEM. The obtained results are compared with analytical solutions to express the efficacy of the methods.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.10a
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• pp.153-160
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• 1995

Mixed finite element formulations for incompressible materials show pressure oscillations or pressure modes in four-node quadrilateral elements. The criterion for the stability in the pressure solution is the so-called Babufka-Brezzi stability condition, and the four-node elements based on mixed variational principles do not appear to satisfy this condition. In this study, a pressure continuity residual based on the pressure discontinuity at element edges is used to study the stabilization of pressure solutions in bilinear displacement-constant pressure four-node quadrilateral elements. It is shown that the pressure solutions, although stable, exhibit sensitivity to the stabilization parameters.

• 한국기계연구소 소보
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• s.19
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• pp.15-21
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• 1989

• Computational Structural Engineering
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• v.8 no.4
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• pp.189-198
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• 1995

The conventional finite element formulations for incompressible materials show pressure oscillations or pressure modes in four-node quadrilateral elements of commonly used displacement and pressure interpolations. The criterion for the stability in the pressure solution is the so-called Babugka-Brezzi stability condition, and the above elements do not satisfy this condition. In this study, a pressure continuity residual based on the pressure discontinuity at element interfaces is used to study the stabilization of pressure solutions in bilinear displacement-constant pressure four-node quadrilateral elements. This pressure residual is implemented in Q1P0 element derived from the conventional incompressible elasticity. The pressure solutions can be stable with the pressure residual though they exhibit sensitivity to the stabilization parameters. Parametric study for the solution stabilization is also discussed.

• Ocean Systems Engineering
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• v.1 no.3
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• pp.207-222
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• 2011

A stabilized incompressible smoothed particles hydrodynamics (ISPH) method is utilized to simulate free falling rigid body into water domain. Both of rigid body and fluid domain are modeled by SPH formulation. The proposed source term in the pressure Poisson equation contains two terms; divergence of velocity and density invariance. The density invariance term is multiplied by a relaxed parameter for stabilization. In addition, large eddy simulation with Smagorinsky model has been introduced to include the eddy viscosity effect. The improved method is applied to simulate both of free falling vessels with different materials and water entry-exit of horizontal circular cylinder. The applicability and efficiency of improved method is tested by the comparisons with reference experimental results.

• Structural Engineering and Mechanics
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• v.6 no.6
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• pp.711-725
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• 1998

Mixed finite element formulations for incompressible materials show pressure oscillations or pressure modes in four-node quadrilateral elements. The criterion for the stability in the pressure solution is the so-called Babu$\check{s}$ka-Brezzi stability condition, and the four-node elements based on mixed variational principles do not appear to satisfy this condition. In this study, a pressure continuity residual based on the pressure discontinuity at element edges proposed by Hughes and Franca is used to study the stabilization of pressure solutions in bilinear displacement-constant pressure four-node quadrilateral elements. Also, a solid mechanics problem is presented by which the stability of mixed elements can be studied. It is shown that the pressure solutions, although stable, are shown to exhibit sensitivity to the stabilization parameters.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.7
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• pp.1341-1350
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• 1992

This paper addresses the practical problem of finding a useful strain energy function of the incompressible rubberlike materials. It examines methods by which the form of the functions are determined and shows how the selection of experimental data influences the resulting form of the functions. From this information, an optimal choice of the form of energy functions becomes possible. Phenomenological theories used in this paper are limited to elastic, incompressible material models. Due to the nature of the phenomenological methods, these theories are accurate only for the materials treated. However, they serve as a starting basis for the study of more complicated material behaviors.

• Fibers and Polymers
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• v.2 no.1
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• pp.140-143
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• 2001

To better understand the formation of necking in drawing processes of fibers, strain distributions during drawing processes have been analyzed. For simplicity, one-dimensional incompressible steady flow at a constant temperature was assumed and quasi-static model was used. To describe mechanical properties of solid polymers, non-linear visco-plastic material properties were assumed using the power law type hardening and rate-sensitive equation. The effects of various parameters on the neck formation were matematically analyzed. As material property parameters, strain-hardening parameter, visco-elastic coefficient and strain-rate sensitivity were considered and, for process parameters, the drawing ratio and the process length were considered. It was found that rate-insensitive materials do not reach a steady flow state and the rate-sensitivity plays a key role to have a steady flow. Also, the neck formation is mainly affected by material properties, especially for the quasi-static model. If the process length changes, the strain distribution was found to be proportionally re-distributed along the process line by the factor of the total length change.

• Advances in aircraft and spacecraft science
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• v.5 no.3
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• pp.295-318
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• 2018

This research studies thermo-elastic behavior of rotating micro discs that are employed in various micro devices such as micro gas turbines. It is assumed that material is functionally graded with a variable profile thickness, density, shear modulus and thermal expansion in terms of radius of micro disc and as a power law function. Boundary condition is considered fixed-free with uniform thermal loading and elastic field is symmetric. Using incompressible material's constitutive equation, we extract governing differential equation of four orders; to solution this equation, we utilize general differential quadrature (GDQ) method and the results are schematically pictured. The obtained result in a particular case is compared with another work and coincidence of results is shown. We will find out that surface effect tends to split micro disc's area to compressive and tensile while nonlocal parameter tries to converge different behaviors with each other; this convergence feature make FGIMs capable to resist in high temperature and so in terms of thermo-elastic behavior we can suggest, using FGIMs in micro devices such as micro turbines (under glass transition temperature).