Design of functionally graded composite structures in the presence of stress constraints

Lipton, Robert

doi:10.1016/s0020-7683(02)00129-4

Cited by 47 publications

(21 citation statements)

References 17 publications

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“…Effective design of the various layers in FGM makes minimum heat diffusion through thickness with maximum thermal insulation [57]. Functionally graded materials are considered to have smooth spatial variation of microstructure and homogenized material properties [26]. This structural variation improves the compressive strength and there is enhancement in the fracture and fatigue strength.…”

Section: Functionally Graded Compositesmentioning

confidence: 99%

Hybrid Carbon-Carbon Ablative Composites for Thermal Protection in Aerospace

Sanoj

Kandasubramanian

2014

Journal of Composites

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Composite materials have been steadily substituting metals and alloys due to their better thermomechanical properties. The successful application of composite materials for high temperature zones in aerospace applications has resulted in extensive exploration of cost effective ablative materials. High temperature heat shielding to body, be it external or internal, has become essential in the space vehicles. The heat shielding primarily protects the substrate material from external kinetic heating and the internal insulation protects the subsystems and helps to keep coefficient of thermal expansion low. The external temperature due to kinetic heating may increase to about maximum of 500 ∘ C for hypersonic reentry space vehicles while the combustion chamber temperatures in case of rocket and missile engines range between 2000 ∘ C and 3000 ∘ C. Composite materials of which carbon-carbon composites or the carbon allotropes are the most preferred material for heat shielding applications due to their exceptional chemical and thermal resistance.

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Section: Functionally Graded Compositesmentioning

confidence: 99%

Hybrid Carbon-Carbon Ablative Composites for Thermal Protection in Aerospace

Sanoj

Kandasubramanian

2014

Journal of Composites

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“…These authors pointed out two important facts about dealing with stress constraint in the layout optimization of continuum structures: (a) the need for taking into account the stress in the microstructure and (b) the stress singularity phenomenon (SSP). The stress in the microstructure was also treated by Lipton [29], who presented a formulation to design functionally graded reinforced shafts subjected to torsional loads, and by Allaire et al [30], who applied topology optimization to minimize an integral of the stress over the domain. The stress singularity phenomenon or SSP, pointed out by Sved and Ginos [10], occurs in layout optimization problems when the material volume fraction of a region in the structure tends to vanish and the micro-stress in this region remains finite.…”

Section: Problem Formulationmentioning

confidence: 99%

“…It is important to note that, differently from the layout (0-1) problem, the material distribution problem can be defined to avoid the stress singularity phenomenon because the material does not vanish, and thus, every point of the extended design domain can have finite stress. This approach was adopted by Lipton [29]. Therefore, to avoid stress singularity phenomenon, a unique stress failure criterion is proposed based on the arithmetic mean of the Von Mises stress:…”

Section: Problem Formulationmentioning

confidence: 99%

Optimization of material distribution in functionally graded structures with stress constraints

Stump

Silva

Paulino

2006

Commun. Numer. Meth. Engng.

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SUMMARYThis work describes a topology optimization framework to design the material distribution of functionally graded structures considering mechanical stress constraints. The problem of interest consists in minimizing the volumetric density of a material phase subjected to a global stress constraint. Due to the existence of microstructure, the micro-level stress is considered, which is computed by means of a mechanical concentration factor using a p-norm of the Von Mises stress criterium (applied to the micro-level stress). Because a 0-1 (void-solid) material distribution is not being sought, the singularity phenomenon of stress constraint does not occur as long as the material at any point of the medium does not vanish and it varies smoothly between material 1 and material 2. To design a smoothly graded material distribution, a material model based on a non-linear interpolation of the Hashin-Strikhman upper and lower bounds is considered. Consistently with the framework adopted here in, the so-called 'continuous approximation of material distribution' approach is employed, which considers a continuous distribution of the design variable inside the finite element. As examples, the designs of functionally graded disks subjected to centrifugal body force are presented. The method generates smooth material distributions, which are able to satisfy the stress constraint.

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“…Later on, these results were extended by Grabovsky and Kohn [14] showing that the Vigdergauz microstructure was actually minimizing the stress concentrations. More recently, Lipton [22] and Lipton and Stuebner [23], [24] provided some analytical and numerical results for functionally graded composites and for composite structures undergoing stress constraints. They proposed an inverse homogenization approach based on the minimization of some modulation functions connecting the macroscopic stress to the local stress fluctuations at microscale.…”

Section: Introductionmentioning

confidence: 99%

Shape optimization of microstructural designs subject to local stress constraints within an XFEM-level set framework

Noël

Duysinx

2016

Struct Multidisc Optim

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The present paper investigates the tailoring of bimaterial microstructures minimizing their local stress field exploiting shape optimization. The problem formulation relies on the extended finite element method (XFEM) combined with a level set representation of the geometry, to deal with complex microstructures and handle large shape modifications while working on fixed meshes. The homogenization theory, allowing extracting the behavior of periodic materials built from the repetition of a representative volume element (RVE), is applied to impose macroscopic strain fields and periodic boundary conditions to the RVE. Classical numerical homogenization techniques are adapted to the selected XFEM-level set framework. Following previous works on analytical sensitivity analysis [31], the scope of the developed approach is extended to tackle the problem of stress objective or constraint functions. Finally, the method is illustrated by revisiting 2D classical shape optimization examples: finding the optimal shapes of single or multiple inclusions in a microstructure while minimizing its local stress field.

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Design of functionally graded composite structures in the presence of stress constraints

Cited by 47 publications

References 17 publications

Hybrid Carbon-Carbon Ablative Composites for Thermal Protection in Aerospace

Hybrid Carbon-Carbon Ablative Composites for Thermal Protection in Aerospace

Optimization of material distribution in functionally graded structures with stress constraints

Shape optimization of microstructural designs subject to local stress constraints within an XFEM-level set framework

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