Closed-form effective elastic constants of frame-like periodic cellular solids by a symbolic object-oriented finite element program

Sam, Pisith; Nanakorn, Pruettha; Theerakittayakorn, Kasem; Suttakul, Pana

doi:10.1007/s10999-016-9342-5

Cited by 14 publications

(14 citation statements)

References 59 publications

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“…( 2) using Young's modulus as the considered stiffness. The results obtained from this study and the related works are 0.35, 0.34 30 , 0.33 31 , and 0.35 32 . These results are well consistent and confirm the experimental results in this study.…”

Section: Resultssupporting

confidence: 62%

“…The AM parts with a pattern orientation of 0/60 Experimental validation. Since an infill specimen with a triangular pattern can be treated as a lattice structure with triangular unit cells, the effective Young's modulus of such a lattice can be predicted using the closed form obtained from the literature 30 . The specimen with the unenclosed sidewalls and pattern orientation of 0/60 degrees, as shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…Figure 6 shows a lattice structure with triangular unit cells, where l denotes the characteristic length of the unit cells and b and t denote the width and thickness, respectively. These significant parameters can be used to compute the effective Young's modulus of lattice structures with triangular unit cells obtained from the literature 30 , i.e., where E *…”

Section: Methodsmentioning

confidence: 99%

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Effect of print parameters on additive manufacturing of metallic parts: performance and sustainability aspects

Fongsamootr

Thawon

Tippayawong

et al. 2022

Sci Rep

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In this study, the effects of print parameters on the mechanical properties of additively manufactured metallic parts were investigated using a tensile test. The 17-4 PH stainless steel specimens with two print parameters, including infill density and pattern orientation, were fabricated by additive manufacturing (AM) using the bound metal deposition (BMD) technique. The mechanical properties considered in this study are the Young’s modulus and ultimate tensile strength. The results demonstrate that the pattern orientations do not affect the Young’s modulus of the infill specimen with the triangular pattern. In contrast, the ultimate strength significantly varies depending on the pattern orientations, where the samples with the pattern orientation of zero degrees yield the best ultimate strength. In fact, the mechanical properties of infill specimens increase with their infill density. However, when operating cost and time are considered, an index for estimating performance and sustainability is consequently established. The relationship between the normalized ultimate strength of an infill specimen and the relative density is defined as the weight efficiency. The index for assessing a sustainable product is characterized by the weight efficiency versus sustainable parameter(s). The index can help end users select an appropriate infill density for AM products by considering the operating cost and time. Different cost models, including material-only costs, direct costs, and total costs, can be included in the index model to assess a sustainable product in a particular cost context.

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Section: Resultssupporting

confidence: 62%

Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Effect of print parameters on additive manufacturing of metallic parts: performance and sustainability aspects

Fongsamootr

Thawon

Tippayawong

et al. 2022

Sci Rep

Self Cite

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“…An advantage of using symbolic computation is that it eliminates cases of roundoff errors in intermediate calculations since parameter variables are carried throughout the calculations using infinite precision arithmetic [1][2][3]. However, in some cases, using symbolic computations can lead to slower execution times depending on the program used and the process [4][5][6]. Symbolic computation has been used and proposed for solving many different problems [7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Comparison of Symbolic Computations for Solving Linear Delay Differential Equations Using the Laplace Transform Method

Sherman

Kerr

González-Parra

2022

MCA

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In this paper, we focus on investigating the performance of the mathematical software program Maple and the programming language MATLAB when using these respective platforms to compute the method of steps (MoS) and the Laplace transform (LT) solutions for neutral and retarded linear delay differential equations (DDEs). We computed the analytical solutions that are obtained by using the Laplace transform method and the method of steps. The accuracy of the Laplace method solutions was determined (or assessed) by comparing them with those obtained by the method of steps. The Laplace transform method requires, among other mathematical tools, the use of the Cauchy residue theorem and the computation of an infinite series. Symbolic computation facilitates the whole process, providing solutions that would be unmanageable by hand. The results obtained here emphasize the fact that symbolic computation is a powerful tool for computing analytical solutions for linear delay differential equations. From a computational viewpoint, we found that the computation time is dependent on the complexity of the history function, the number of terms used in the LT solution, the number of intervals used in the MoS solution, and the parameters of the DDE. Finally, we found that, for linear non-neutral DDEs, MATLAB symbolic computations were faster than Maple. However, for linear neutral DDEs, which are often more complex to solve, Maple was faster. Regarding the accuracy of the LT solutions, Maple was, in a few cases, slightly better than MATLAB, but both were highly reliable.

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“…Additionally, other works have been presented in which closed‐form integration of the stiffness matrix were obtained . Recently, closed‐form of elastic constants in frame‐like periodic cellular solids have been analytically derived using symbolic objetc‐oriented finite element program in MATLAB [14,16]. A version of hp‐FEM algorithm is implemented by Hakula and Tuominen using the software Wolfram Mathematica as the programming environment.…”

Section: Introductionmentioning

confidence: 99%

A finite element elasticity programming in Mathematica software

Cecílio

Santos

2018

Comp Applic In Engineering

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Modern software's allow computers to perform symbolic calculations in addition to simple numerical computations for which they were originally designed. This fact opens new possibilities in numerical simulation. In this paper a finite element implementation using the commercial software Wolfram Mathematica is used to solve a plane stress elasticity problem. The code adaptability from the provided examples to more challenging problems can easily be performed using the present code. Numerical examples with post‐processing illustrates the new tool and its flexibility. It has been proven in this study the feasibility of Wolfram Mathematica in learning and programming finite element methods for the solution of two‐dimensional problems in elasticity.

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Closed-form effective elastic constants of frame-like periodic cellular solids by a symbolic object-oriented finite element program

Cited by 14 publications

References 59 publications

Effect of print parameters on additive manufacturing of metallic parts: performance and sustainability aspects

Effect of print parameters on additive manufacturing of metallic parts: performance and sustainability aspects

Comparison of Symbolic Computations for Solving Linear Delay Differential Equations Using the Laplace Transform Method

A finite element elasticity programming in Mathematica software

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