Numerical Study of Frequency and Deflection Responses of Natural Fiber (Luffa) Reinforced Polymer Composite and Experimental Validation

ABSTRACT

The natural fiber (Luffa cylindrica fiber) reinforced epoxy composite has been fabricated and their structural responses (frequency and deflection) have been computed experimentally and numerically first time using the corresponding experimental elastic properties. The numerical responses are obtained with the help of an in-house MATLAB code developed based on the higher order finite element (FE) model. The completeness of the model has been examined by comparing the current FE solutions (frequency and the central deflection) with the reference as well as in-house experimental data. The effect of fiber volume fractions on the elastic properties is verified for four different weight percentage of treated Luffa fiber (0%, 3.2%, 6.4%, and 9.6%). Finally, the inclusive behavior of the current higher order FE model and the corresponding influence of the significant design parameter of Luffa fiber-reinforced composite structure have been debated by solving different numerical examples.

摘要

利用自制的天然纤维（丝瓜纤维）增强环氧复合材料，利用相应的实验弹性特性，首次对其结构响应（频率和挠度）进行了实验和数值计算。借助于基于高阶有限元模型开发的内部MATLAB代码，获得了数值响应，并通过将当前有限元解（频率和中心挠度）与参考值进行比较，检验了模型的完备性。作为内部实验数据。纤维体积分数对弹性性能的影响验证了四种不同重量百分比的经处理的丝瓜纤维（0、3.2、6.4和9.6%）。最后，通过求解不同的数值例子，讨论了当前高阶有限元模型的包容行为以及Luffa纤维增强复合材料结构的重要设计参数的相应影响

KEYWORDS:

• Natural frequency
• static deflection
• Luffa cylindrical
• Epoxy
• Natural fiber-reinforced composite
• HSDT
• finite element analysis

关键词:

• 固有频率
• 静态挠度
• 环氧树脂
• 天然纤维增强复合材料
• 有限元分析

List of abbreviations

Terminologies	=
HSDT	=	Higher order shear deformation theory
FEM	=	Finite element method
DOF	=	Degrees of freedom
Mathematical formulation	=
${\xi }_1,{\xi }_2$, and$\xi$	=	Three mutually perpendicular axis in Cartesian coordinate system
$u_0,v_0,w_0$	=	Mid plane displacement along ${\xi }_1,{\xi }_2$, and$\xi$ direction
$a,b,h$	=	Length, breadth, and thickness of the panel (m)
${\varphi }_1,{\varphi }_2$	=	Rotations about ${\xi }_2,{\xi }_1$ direction
${\psi }_1,{\psi }_2,{\theta }_1,{\theta }_2$	=	Higher order terms of Taylor series expansion
$E$	=	Young’s modulus (N/m2)
$v$	=	Poisson’s ratios
$U$	=	Total strain energy
$V$	=	Total kinetic energy
$W$	=	Work done
$[K]$	=	Global stiffness matrix
$[M]$	=	Global mass matrix