Dynamics of thick hygrothermal viscoelastic composite laminates through finite element method

Assie, Amr E.,Mahmoud, Fatin F. Techno-Press 2004 Structural Engineering and Mechanics, An Int'l Jou Vol.17 No.5

An uncoupled computational model for analyzing the hygrothermal dynamic response of composite laminates has been developed. The constitutive equations, expressed in an integral form, and involving relaxation moduli are adopted, to describe the non-aging hygrothermorheologically simple materials. A Prony series represents the relaxation moduli is exploited in order to derive a recursive relationship, and thereby eliminate the storage problem that arises when dealing with material possessing memory. The problem is formulated in a descritized variational form. Mindlin and higher order finite elements are employed for spatial descretization, while the Newmark average acceleration scheme is exploited for temporal descritization. The adopted recursive formula uses only the details of the previous event to compute the details of the current one. Numerical results of the displacement fields of both thin and thick viscoelastic laminates problems are discussed to show up the effectiveness of Mindlin and higher-order shear theories.

Dynamic analysis of porous functionally graded layered deep beams with viscoelastic core

Amr Assie,Şeref D. Akbaş,Abdallah M. Kabeel,Alaa A. Abdelrahman,Mohamed A Eltaher 국제구조공학회 2022 Steel and Composite Structures, An International J Vol.43 No.1

In this study, the dynamic behavior of functionally graded layered deep beams with viscoelastic core is investigated including the porosity effect. The material properties of functionally graded layers are assumed to vary continuously through thickness direction according to the power-law function. To investigate porosity effect in functionally graded layers, three different distribution models are considered. The viscoelastically cored deep beam is exposed to harmonic sinusoidal load. The composite beam is modeled based on plane stress assumption. The dynamic equations of motion of the composite beam are derived based on the Hamilton principle. Within the framework of the finite element method (FEM), 2D twelve –node plane element is exploited to discretize the space domain. The discretized finite element model is solved using the Newmark average acceleration technique. The validity of the developed procedure is demonstrated by comparing the obtained results and good agreement is detected. Parametric studies are conducted to demonstrate the applicability of the developed methodology to study and analyze the dynamic response of viscoelastically cored porous functionally graded deep beams. Effects of viscoelastic parameter, porosity parameter, graduation index on the dynamic behavior of porous functionally graded deep beams with viscoelastic core are investigated and discussed. Material damping and porosity have a significant effect on the forced vibration response under harmonic excitation force. Increasing the material viscosity parameters results in decreasing the vibrational amplitudes and increasing the vibration time period due to increasing damping effect. Obtained results are supportive for the design and manufacturing of such type of composite beam structures.

Effect of loading and lamination parameters on the optimum design of laminated plates

A. E. Assie,A. M. Kabeel,F. F. Mahmoud 대한기계학회 2011 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.25 No.5

This paper illustrates the effect of loading conditions and lamination parameters on the optimum design of the laminated composite plates. Optimum design procedure based on the flexibility criterion is presented in this paper. The objective is to determine the optimum thickness of the laminate layers and its optimum orientations without exhibiting any failure. The finite element method based on Mindlin plate theory is used in conjunction with an optimization method in order to determine the optimum design. Newmark implicit time integration scheme is used to discretize the time domain and calculate the transient response of the laminated plate. Exterior penalty method is exploited as a constrained minimization technique. For this purpose, four numerical examples are presented to figure out the effects of dynamic loading profile, boundary conditions, number of layers, and degree of orthotropy on the optimum weight design.

Behavior of a viscoelastic composite plates under transient load

A. E. Assie,M. A. Eltaher,F. F. Mahmoud 대한기계학회 2011 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.25 No.5

An efficient numerical algorithm for analyzing dynamic response of orthotropic viscoelastic composite laminates has been developed in the time domain. The integral form of the constitutive laws is exploited. Generalized Wiechert model is adopted to simulate the viscoelasticity of the structure Mindlin-Reissner plate theory is utilized in finite element formulation employing the consistent mass matrix. The proposed algorithm is incorporated in the framework of the finite element based on the displacement model. Newmark Constant average acceleration method is used for integration equation of motion. The developed recurrence formula permits the new time solutions to be evaluated using only previous time values. The developed solution technique is applied to orthotropic plate under two types of force,which are the step-pulse and sin-pulse force.

Static and stress analyses of bi-directional FG porous plate using unified higher order kinematics theories

Salwa Mohamed,Amr E. Assie,Nazira Mohamed,Mohamed A Eltaher 국제구조공학회 2022 Steel and Composite Structures, An International J Vol.45 No.3

This article aims to investigate the static deflection and stress analysis of bi-directional functionally graded porous plate (BDFGPP) modeled by unified higher order kinematic theories to include the shear stress effects, which not be considered before. Different shear functions are described according to higher order models that satisfy the zero-shear influence at the top and bottom surfaces, and hence refrain from the need of shear correction factor. The material properties are graded through two spatial directions (i.e., thickness and length directions) according to the power law distribution. The porosities and voids inside the material constituent are described by different cosine functions. Hamilton’s principle is implemented to derive the governing equilibrium equation of bi-directional FG porous plate structures. An efficient numerical differential integral quadrature method (DIQM) is exploited to solve the coupled variable coefficients partial differential equations of equilibrium. Problem validation and verification have been proven with previous prestigious work. Numerical results are illustrated to present the significant impacts of kinematic shear relations, gradation indices through thickness and length, porosity type, and boundary conditions on the static deflection and stress distribution of BDFGP plate. The proposed model is efficient in design and analysis of many applications used in nuclear, mechanical, aerospace, naval, dental, and medical fields.

Dynamic of thick hygrouthermal viscoelastic composite laminates through finite element method

Fatin F. Mahmoud,Amr E. Assie 국제구조공학회 2004 Structural Engineering and Mechanics, An Int'l Jou Vol.17 No.5

Buckling of 2D FG Porous unified shear plates resting on elastic foundation based on neutral axis

Rabab Shanab,Salwa Mohamed,Mohammed Y. Tharwan,Amr E. Assie,Mohamed A Eltaher 국제구조공학회 2022 Steel and Composite Structures, An International J Vol.45 No.5

The critical buckling loads and buckling modes of bi-directional functionally graded porous unified higher order shear plate with elastic foundation are investigated. A mathematical model based on neutral axis rather than midplane is developed in comprehensive way for the first time in this article. The material constituents form ceramic and metal are graded through thickness and axial direction by the power function distribution. The voids and cavities inside the material are proposed by three different porosity models through the thickness of plate. The constitutive parameters and force resultants are evaluated relative to the neutral axis. Unified higher order shear plate theories are used to satisfy the zero-shear strain/stress at the top and bottom surfaces. The governing equilibrium equations of bi-directional functionally graded porous unified plate (BDFGPUP) are derived by Hamilton’s principle. The equilibrium equations in the form of coupled variable coefficients partial differential equations is solved by using numerical differential integral quadrature method (DIQM). The validation of the present model is presented and compared with previous works for bucking. Deviation in buckling loads for both mid-plane and neutral plane are developed and discussed. The numerical results prove that the shear functions, distribution indices, boundary conditions, elastic foundation and porosity type have significant influence on buckling stability of BDFGPUP. The current mathematical model may be used in design and analysis of BDFGPU used in nuclear, mechanical, aerospace, and naval application.

Damped forced vibration analysis of layered functionally graded thick beams with porosity

Ali Alnujaie,Şeref D. Akbaş,Mohamed A Eltaher,Amr E. Assie 국제구조공학회 2021 Smart Structures and Systems, An International Jou Vol.27 No.4

The following article presents the damped forced vibration of layered functionally graded thick beams including material porosities. In case of very thick beams, beam theories fail to satisfy boundary conditions and to predict the mechanical response accurately. So, the two-dimensional (2D) plane continuum model is exploited to model a thick functionally graded layered beam. The beam is composed from three- layers with functionally graded porous materials. The porosity is described by three different distribution models through the layer thickness. Applied forces to the functionally graded beam are assumed to be sinusoidal harmonic point load in time domain. The Kelvin—Voigt viscoelastic constitutive model is used to simulate damping effect. The governing equations are obtained by using Lagrange's equations. In frame of finite element analysis, twelve .node 2D plane element is exploited to discretize the space domain of thick beam. In the solution of the dynamic problem, the Newmark average acceleration method is used. Numerical studies illustrate effects of porosity distribution, stacking sequence, and graduation constant on the dynamic responses of layered functionally graded porous thick beams. The results show that the porosity function, stacking sequences and the damping ratio have a vital role in dynamic response of functionally graded beams. The proposed model can be used in nuclear, marine, and aerospace technologies.

On vibrations of functionally graded carbon nanotube (FGCNT) nanoplates under moving load

Alaa A. Abdelrahman,Ismail Esen,Mohammed Y. Tharwan,Amr Assie,Mohamed A Eltaher Techno-Press 2024 Advances in nano research Vol.16 No.4

This article develops a nonclassical size dependent nanoplate model to study the dynamic response of functionally graded carbon nanotube (FGCNT) nanoplates under a moving load. Both nonlocal and microstructure effects are incorporated through the nonlocal strain gradient elasticity theory. To investigate the effect of reinforcement orientation of CNT, four different configurations are studied and analysed. The FGM gradation thorough the thickness direction is simulated using the power law. In the context of the first order shear deformation theory, the dynamic equations of motion and the associated boundary conditions are derived by Hamilton's principle. An analytical solution of the dynamic equations of motion is derived based on the Navier methodology. The proposed model is verified and compared with the available results in the literature and good agreement is found. The numerical results show that the dynamic performance of FGCNT nanoplates could be governed by the reinforcement pattern and volume fraction in addition to the non-classical parameters and the moving load dimensionless parameter. Obtained results are reassuring in design and analysis of nanoplates reinforced with CNTs.

Dynamics of perforated higher order nanobeams subject to moving load using the nonlocal strain gradient theory

Alaa A. Abdelrahman,Ismail Esen,Cevat Özarpa,Ramy Shaltout,Mohamed A Eltaher,Amr E. Assie 국제구조공학회 2021 Smart Structures and Systems, An International Jou Vol.28 No.4

The goal of this manuscript is to develop a nonclassical size dependent model to study and analyze the dynamic behaviour of the perforated Reddy nanobeam under moving load including the length scale and microstructure effects, that not considered before. The kinematic assumption of the third order shear deformation beam theory in conjunction with modified continuum constitutive equation of nonlocal strain gradient (NLSG) elasticity are proposed to derive the equation of motion of nanobeam included size scale (nonlocal) and microstructure (strain gradient) effects. Mathematical expressions for the equivalent geometrical parameters due to the perforation process of regular squared pattern are developed. Based on the virtual work principle, the governing equations of motion of perforated Reddy nanobeams are derived. Based on Navier's approach, an analytical solution procedure is developed to obtain free and forced vibration response under moving load. The developed methodology is verified and checked with previous works. Impacts of perforation, moving load velocity, microstructure parameter and nonlocal size scale effects on the dynamic and vibration responses of perforated Reddy nanobeam structures have been investigated in a wide context. The obtained results are supportive for the design of MEMS/NEMS structures such as frequency filters, resonators, relay switches, accelerometers, and mass flow sensors, with perforation.