Applicability extent of 2-D heat equation for numerical analysis of a multiphysics problem

Khawaja, Hassan Abbas

doi:10.1063/1.4972667

Cited by 5 publications

(4 citation statements)

References 17 publications

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“…The Finite Difference Method (FDM) is a numerical method for solving differential equations such as the two-dimensional wave [22][23][24][25][26][27], as given in Equation 1. This method approximates the differentials by discretizing the dependent variables (strain) in the independent variable domains (space and time, in this case) [27][28][29]. Each discretized value of the dependent variable is referred to as a nodal value.…”

Section: Finite Difference Methods (Matlab®)mentioning

confidence: 99%

Strain Wave Analysis in Carbon-Fiber-Reinforced Composites subjected to Drop Weight Impact Test using ANSYS®

2021

IJM

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Composite materials are becoming more popular in technological applications due to the significant weight savings and strength these materials offer compared to metallic materials. In many of these practical situations, the structures suffer from drop impact loads. Materials and structures significantly change their behavior when submitted to impact loading conditions as compared to quasi-static loading. The present work is devoted to investigating the elastic strain wave in Carbon-Fiber-Reinforced Polymers (CFRP) when subjected to a drop test. A novel drop weight impact test experimental method evaluates parameters specific to 3D composite materials during the study. A strain gauge rosette is employed to record the kinematic on the composites' surface. Experimental results were validated through numerical analysis by FDM Numerical Simulations in MATLAB® and ANSYS® Explicit Dynamic Module. A MATLAB® code was developed to solve wave equation in a 2-D polar coordinate system by discretizing through a Forward-Time Central-Space (FTCS) Finite Difference Method (FDM). Another FEA analysis was performed in ANSYS® Workbench Explicit Dynamics module to simulate the elastic waves produced during the DWIT.The study demonstrates that the elastic waves generated upon impact with a 33 g steel ball from a height of 1 m in a quasi-isotropic CFRP sheet give a strain wave frequency of 205 Hz and finish in almost 0.015 s due to a significant damping effect. Numerical simulations were in good agreement with the experimental findings.

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Section: Finite Difference Methods (Matlab®)mentioning

confidence: 99%

Strain Wave Analysis in Carbon-Fiber-Reinforced Composites subjected to Drop Weight Impact Test using ANSYS®

2021

IJM

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“…The FDM is a numerical method for solving differential equations such as the twodimensional wave [34,35] and heat equation [36][37][38], as given in Equations ( 1) and ( 4). This method approximates the differentials by discretizing the dependent variables (strain and temperature) in the independent variable domains (space and time) [39][40][41]. Each discretized value of the dependent variable is referred to as a nodal value.…”

Section: Finite Difference Methods (Matlab ® )mentioning

confidence: 99%

Thermoelastic Investigation of Carbon-Fiber-Reinforced Composites Using a Drop-Weight Impact Test

et al. 2020

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Composite materials are becoming more popular in technological applications due to the significant weight savings and strength offered by these materials compared to metallic materials. In many of these practical situations, the structures suffer from drop-impact loads. Materials and structures significantly change their behavior when submitted to impact loading conditions compared to quasi-static loading. The present work is devoted to investigating the thermal process in carbon-fiber-reinforced polymers (CFRP) subjected to a drop test. A novel drop-weight impact test experiment is performed to evaluate parameters specific to 3D composite materials. A strain gauge rosette and infrared thermography are employed to record the kinematic and thermal fields on the composites’ surfaces. This technique is nondestructive and offers an extensive full-field investigation of a material’s response. The combination of strain and infrared thermography data allows a comprehensive analysis of thermoelastic effects in CFRP when subjected to impacts. The experimental results are validated using numerical analysis by developing a MATLAB® code to analyze whether the coupled heat and wave equation phenomenon exists in a two-dimensional polar coordinate system by discretizing through a forward-time central-space (FTCS) finite-difference method (FDM). The results show the coupling has no significant impact as the waves generated due to impact disappears in 0.015 s. In contrast, heat diffusion happens for over a one-second period. This study demonstrates that the heat equation alone governs the CFRP heat flow process, and the thermoelastic effect is negligible for the specific drop-weight impact load.

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“…The size and number of mesh grid points define the extent of calculations. Considering the symmetry of the cases and specific physical assumptions, realistic and complex 3-D problems can be degenerated to less complex 2-D problems, therefore, providing an offering of a considerable CPU memory consumption gain [31].…”

Section: Incompressible Navier Stokes Equationsmentioning

confidence: 99%

Conjugate Heat Transfer Model Based on SIMPLE and Coupled Energy and Heat Equations

2021

IJM

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In this study, a numerical weak coupling strategy for the modeling of a conjugate heat transfer phenomenon is considered. Where the incompressible Navier Stokes equations are solved using the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) as a first step, and then the heat conduction equation for solid is solved in a second step considering the convective velocity field resulting from the first step. A finite-difference approach is used for both discretized time and spatial operators. In this paper, a two-dimensional simulation case study of a steady uniform stream wise flow around heated rectangular and triangle solids is presented. The simulation is forward in time until the steady-state regime is reached as the residuals converge and tend to zero. The spatial analysis of the temperature is obtained through the numerical resolution of the incompressible Navier Stokes, energy equation, and the heat diffusion equation for the fluid and solid media, respectively. The results show the temperature, velocity, and pressure fields in the space domain. The coding is conducted in MATLAB®, and the flow chart of the method is provided. It was noted that the convection was more dominant than the diffusion.

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Applicability extent of 2-D heat equation for numerical analysis of a multiphysics problem

Cited by 5 publications

References 17 publications

Strain Wave Analysis in Carbon-Fiber-Reinforced Composites subjected to Drop Weight Impact Test using ANSYS®

Strain Wave Analysis in Carbon-Fiber-Reinforced Composites subjected to Drop Weight Impact Test using ANSYS®

Thermoelastic Investigation of Carbon-Fiber-Reinforced Composites Using a Drop-Weight Impact Test

Conjugate Heat Transfer Model Based on SIMPLE and Coupled Energy and Heat Equations

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