Total Potential Energy Of System Research Articles

Forced vibration analysis of concrete slabs reinforced by agglomerated SiO2 nanoparticles based on numerical methods

Abstract In this research, forced vibration analysis of a concrete slab reinforced by SiO2 nanoparticles is investigated. The Mori-Tanaka low is used for obtaining the material properties of nano-composite structure and considering agglomeration effects. By means of third order shear deformation theory or Reddy theory, the total potential energy of system is calculated. Also, using Hamilton’s principle, the coupled motion equations are obtained. Based on the harmonic differential quadrature method (HDQM), finite element method (FEM) and Newmark method, the frequency response of system is calculated. The effects of volume percent and agglomeration of SiO2 nanoparticles, boundary conditions and geometrical parameters of structure are shown on the frequency response of system. Results show that with growing the volume percent of SiO2 nanoparticles up to 0.37, the linear frequency of the structure is increased and the maximum dynamic deflection is decreased.

Vibration analysis of concrete foundation armed by silica nanoparticles based on numerical methods

In this study, vibration analysis of a concrete foundation-reinforced by SiO2 nanoparticles resting on soil bed is investigated. The soil medium is simulated with spring constants. Furthermore, the Mori-Tanaka low is used for obtaining the material properties of nano-composite structure and considering agglomeration effects. Using third order shear deformation theory or Reddy theory, the total potential energy of system is calculated and by means of the Hamilton\'s principle, the coupled motion equations are obtained. Also, based an analytical method, the frequency of system is calculated. The effects of volume percent and agglomeration of SiO2 nanoparticles, soil medium and geometrical parameters of structure are shown on the frequency of system. Results show that with increasing the volume percent of SiO2 nanoparticles, the frequency of structure is increased.

Mathematical modeling of smart nanoparticles-reinforced concrete foundations: Vibration analysis

In this research, vibration and smart control analysis of a concrete foundation reinforced by SiO2 nanoparticles and covered by piezoelectric layer on soil medium is investigated. The soil medium is simulated with spring constants and the Mori-Tanaka low is used for obtaining the material properties of nano-composite structure and considering agglomeration effects. With considering first order shear deformation theory, the total potential energy of system is calculated and by means of Hamilton.s principle in three displacement directions and electric potential, the six coupled equilibrium equations are obtained. Also, based an analytical method, the frequency of system is calculated. The effects of applied voltage, volume percent and agglomeration of SiO2 nanoparticles, soil medium and geometrical parameters of structure are shown on the frequency of system. Results show that with applying negative voltage, the frequency of structure is increased.

Elastic properties of chiral carbon nanotubes under oxygen adsorption

This work aims to comprehensively study the effect of oxygen chemisorption on the elastic properties of carbon nanotubes (CNTs). To this end, a molecular mechanics model is used along with the density functional theory (DFT) calculations. This investigation is conducted for oxygenated carbon nanotubes (O-CNTs) with various types of chirality including armchair, zigzag and chiral. On the basis of DFT, the force constants used in the total potential energy of system are calculated. Moreover, Young's modulus and Poisson's ratio of oxygenated graphene sheet (O-graphene) are determined based on the DFT. The results show that by adsorption of oxygen atoms, the stiffness of graphene reduces about 23%. The bending stiffness of O-graphene is obtained corresponding to adsorption on the inside and outside of the nanotubes. It is revealed that for an arbitrary value of diameter, Young's modulus of zigzag O-CNTs is smaller than that of chiral O-CNTs and the latter one is also smaller than that of armchair O-CNTs, while a reverse trend is found for the variation of Poisson's ratio with the chirality.

Discussions on the Two Properties and Applications of Elastic Deformation and Deformation Energy

During the process of elastic deformation, based on first law of thermodynamics, deformation energy value equals to the work done by external forces moving through elastic deformation, which can determine the amount of elastic deformation. According to second law of thermodynamics, the true deformation energy value should be the minimum of all possible deformations, which can determine the distribution rule of elastic deformation. From this, it can be realized that there are some problems existed in the derived process of the minimum potential energy principle. The total potential energy of system remains constant in all of possible elastic deformation. Applying the two characteristics of elastic deformation, a few application problems could be solved expediently.

Analysis of flexible frames by energy search

A geometrically nonlinear finite element formulation based on a moving Eulerian coordinate system is used to predict the structural response of flexible planar frames. The total potential energy of the system is expressed in terms of the strain inducing displacements and parameters that reflect the coupling between axial (tension or compression) and bending effects. A conjugate gradient energy search procedure is employed to minimize directly the total potential energy of the structural system. The method includes the effects of prestressing and prescribing displacements in addition to abrupt changes in geometric configuration due to buckling of compression members and slackening of tension elements. Numerical examples illustrate and verify the accuracy of the technique presented.