Three Kinds օf Porosity օn Functionally Graded Porous Beams


  • Lan Hoang That Ton HCMC University of Architecture



bending behavior, functionally graded porous (FGP) beam, transverse displacement, rotation, simple Timoshenko beam


In this paper, the effects of three types of porosity on bending behavior of functionally graded porous (FGP) beams are studied. The finite element procedure is established and based on the simple Timoshenko beam theory. The results achieved in this paper are presented and compared with other results in the references to verify the feasibility of implementing the formula and writing the Matlab code. On the other hand, this paper can help researchers to have an overview of the bending behavior of the functionally graded porous beams. 

Author Biography

Lan Hoang That Ton, HCMC University of Architecture

(Vietnam, HCMC) - HCMC University of Architecture, Faculty of Civil Engineering, Assistant Professor


O. Carvalho, M. Buciumeanu, G. Miranda, S. Madeira, F.S. Silva, Development of a Method to Produce Fgms by Controlling the Reinforcement Distribution. Materials & Design, 92, 2016, 233-239. DOI:

R. K. Singh, V. Rastogi, A Review on Solid State Fabrication Methods and Property Characterization of Functionally Graded Materials. Materials Today: Proceedings, 2021. DOI:

V. Boggarapu, R. Gujjala, S. Ojha, S. Acharya, P. Venkateswara babu, S. Chowdary et al., State of the Art in Functionally Graded Materials. Composite Structures, 262, 2021, 113596. DOI:

M. Gautam, M. Chaturvedi, Optimization of Functionally Graded Material under Thermal Stresses. Materials Today: Proceedings, 44, 2021, 1520-1523. DOI:

M. Sam, R. Jojith, N. Radhika, Progression in Manufacturing of Functionally Graded Materials and Impact of Thermal Treatment - A Critical Review. Journal of Manufacturing Processes, 68, 2021, 1339-1377. DOI:

Y. Mognhod Bezzie, D. Engida Woldemichael, E. Tefera Chekol, S. Alemneh Admass, S.K. Selvaraj, V. Paramasivam, Effect of Volumetric Fraction Index on Temperature Distribution in Thick-Walled Functionally Graded Material Made Cylinder. Materials Today: Proceedings, 46, 2021, 7442-7447. DOI:

H. Liu, S. Ding, B.F. Ng, Impact Response and Energy Absorption of Functionally Graded Foam Under Temperature Gradient Environment. Composites Part B: Engineering, 172, 2019, 516-532. DOI:

V. N. Burlayenko, H. Altenbach, T. Sadowski, S. D. Dimitrova, A. Bhaskar, Modelling Functionally Graded Materials in Heat Transfer and Thermal Stress Analysis by Means of Graded Finite Elements. Applied Mathematical Modelling, 45, 2017, 422-438. DOI:

Z. Zheng, Y. Yi, X. Bai, A. Nakayama, Functionally Graded Structures for Heat Transfer Enhancement. International Journal of Heat and Mass Transfer, 173, 2021, 121254. DOI:

Y. Xiong, Z. Han, J. Qin, L. Dong, H. Zhang, Y. Wang et al., Effects of Porosity Gradient Pattern on Mechanical Performance of Additive Manufactured Ti-6Al-4V Functionally Graded Porous Structure. Materials & Design, 208, 2021, 109911. DOI:

M. Iasiello, N. Bianco, W.K.S. Chiu, V. Naso, The Effects of Variable Porosity and Cell Size on the Thermal Performance of Functionally-Graded Foams. International Journal of Thermal Sciences, 160, 2021, 106696. DOI:

G. H. Loh, E. Pei, D. Harrison, M.D. Monzón, An Overview of Functionally Graded Additive Manufacturing. Additive Manufacturing, 23, 2018, 34-44. DOI:

S. R. Singiresu, The Finite Element Method in Engineering. Elsevier, 2018.

X. F. Li, A Unified Approach for Analyzing Static and Dynamic Behaviors of Functionally Graded Timoshenko and Euler–Bernoulli Beams. Journal of Sound and Vibration, 318, 2008, 1210-1229. DOI:

D. Wu, W. Gao, D. Hui, K. Gao, K. Li, Stochastic Static Analysis of Euler-Bernoulli Type Functionally Graded Structures. Composites Part B: Engineering, 134, 2018, 69-80. DOI:

I. Katili, T. Syahril, A.M. Katili, Static and Free Vibration Analysis of FGM Beam Based on Unified and İntegrated of Timoshenko’s Theory. Composite Structures, 242, 2020, 112130. DOI:

S.-R. Li, D.-F. Cao, Z.-Q. Wan, Bending Solutions of FGM Timoshenko Beams from Those of the Homogenous Euler–Bernoulli Beams. Applied Mathematical Modelling, 37, 2013, 7077-7085. DOI:

H. L. Ton-That, H. Nguyen-Van, T. Chau-Dinh, A Novel Quadrilateral Element for Analysis of Functionally Graded Porous Plates/Shells Reinforced by Graphene Platelets. Archive of Applied Mechanics, 91, 2021, 2435-2466. DOI:

H. L. Ton-That, The Linear and Nonlinear Bending Analyses of Functionally Graded Carbon Nanotube-Reinforced Composite Plates Based on the Novel Four-Node Quadrilateral Element. European Journal of Computational Mechanics, 29 (1), 2020, 139-172. DOI:

M. Şimşek, T. Kocatürk, Ş.D. Akbaş, Static Bending of a Functionally Graded Microscale Timoshenko Beam Based on the Modified Couple Stress Theory. Composite Structures, 95, 2013, 740-747. DOI:

H. L. Ton-That, A Combined Strain Element to Functionally Graded Structures in Thermal Environment. Acta Polytechnica, 60 (6), 2020, 528-539. DOI:

P. V. Avhad, A.S. Sayyad, Static Analysis of Functionally Graded Composite Beams Curved in Elevation Using Higher Order Shear and Normal Deformation Theory. Materials Today: Proceedings, 21, 2020, 1195-1199. DOI:

D. Chen, J. Yang, S. Kitipornchai, Elastic Buckling and Static Bending of Shear Deformable Functionally Graded Porous Beam. Composite Structures, 133, 2015, 54-61. DOI:

N. V. Viet, W. Zaki, Bending Model for Functionally Graded Porous Shape Memory Alloy/ Poroelastic Composite Cantilever Beams. Applied Mathematical Modelling, 97, 2021, 398-417. DOI:

B. Anirudh, M. Ganapathi, C. Anant, O. Polit, A Comprehensive Analysis of Porous Graphene-Reinforced Curved Beams by Finite Element Approach Using Higher-Order Structural Theory: Bending, Vibration and Buckling. Composite Structures, 222, 2019, 110899. DOI:

G. Marcial, Mechanics of Materials. ed. Purdue University, 2021.




How to Cite

Hoang That Ton, L. (2022). Three Kinds օf Porosity օn Functionally Graded Porous Beams. Journal of Architectural and Engineering Research, 2, 28–35.