Stability analysis of nanocomposite beam on elastic support under axial force

Dissertation for Master's Degree in Mechanical Engineering

Trend: Applied Design

Abstract

In this thesis, stability analysis of composite beam reinforced with carbon nanotubes on elastic support under axial force is investigated is placed The distribution of nanotubes is assumed to be uniform[1]. To determine the properties of materials reinforced with nanotubes, the results of molecular dynamics and laws of mixtures are used. Using Euler-Bernoulli and Timoshenko beam theories and taking into account plane stress assumptions, beam equilibrium equations will be obtained by applying Hamilton's principle. Beam stability equations and boundary conditions will also be obtained by applying elastic bed forces. Then the governing differential equations were generalized by using the quadratic differential method and solved by applying simple support boundary conditions. By setting the determinant of the matrix of critical load coefficients equal to zero, mechanical buckling is obtained. According to the results for the beam reinforced with carbon nanotubes, the amount of dimensionless axial deflection increases with the increase in volume fraction. The accuracy of the results is compared with other existing articles and high accuracy is established between the results of this research and other articles. Keywords: buckling, composite beam, critical load of mechanical buckling, carbon nanotube, generalized square differential method 

Introduction

        The combination of two or more substances with each other so that they are chemically separate and insoluble, and the efficiency and properties of the components of this combination are in a superior position compared to each of its components alone, is called a composite. In other words, composite refers to materials that are mixtures of different materials in form and composition, and their components retain their identity, do not dissolve in each other, and do not mix together. Due to this, composite is different from metal alloy. Therefore, a composite is a combination of at least two chemically distinct materials with a defined interface between each constituent component.

        No one knows when the first composite was made. Perhaps the first composite that mankind dealt with is flower straw. In the old days, they used mud to build houses, but because the mud cracked after drying, they added some straw to fill the holes and prevent the mud from cracking. Perhaps the first composite was made by the Egyptians who mixed some fabric with the wood of the hull in their boats so that the wood would not swell due to getting wet. However, it can be said that composite materials have been accepted as an engineering material in recent years.

        The first task of the field is to surround the reinforcing material so as not to let the reinforcing material disperse. The second task is to protect the reinforcing material against chemical factors, and as we can see in Figure (1-1), the third task is that because the ground material is soft, when force enters the composite material, it is transferred to the reinforcing material by the ground so that the reinforcing material can bear the force. Composites are divided into three main groups based on the type of ground that surrounds the reinforcement and connects them. The international classification of the unit is divided as follows:

1 - Polymer based composites [2]

2 - Metal based composites for making products exposed to wear and friction [3]

3 - Ceramic based composites for making products exposed to thermal loads Ziad[4]

A summary of the properties of these categories is given in table (1-1).

     Polymer based composites are the most important category of composites.A wide range of industries, from high-end industries such as the production of airplane parts to low-end industries such as the production of dishwasher sinks, are produced from polymer-based composites, and currently they occupy 59% of the composites market, and for this reason, they are considered the largest subset of composite materials.

     Polymer-based composites are currently only used to the extent of 1%, in their birthplace, i.e., the aerospace industry, and the majority of the rest is in the construction and transportation industries. and quotes are used. In fact, the development of the production technology of polymer-based composites has made it possible for most industries to benefit from the unique advantages of these materials.

     Weight reduction of the built structure due to the architecture that can be changed according to the design, safety against the phenomenon of corrosion, the ability to withstand cyclic loads and very good resistance against the phenomenon of fatigue, the simplicity of production methods, the possibility of producing very complex shapes with very easy, efficient and cost-effective methods, the ease of repair and troubleshooting processes, the coefficient Low thermal expansion and suitable thermal insulation, electrical insulation, improved connections and the possibility of integrated production, very suitable vibration characteristics and resistance to the phenomenon of resonance in vibrations compared to metals and easy assembly are other characteristics of polymer-based composites. Polymers, ceramics and metals are divided.

1-2-1- Polymers

Polymers, known as resin, are the most common base materials and are usually divided into two general groups: thermoset and thermoplastic.

Thermoset polymers have a low density and are easier to produce because they are expensive. They are lower in molten state and are easily spread on the fibers. These types of polymers include epoxy and polyester. These polymers are not recyclable. Low strain until the moment of failure, high moisture absorption and resistance to solvents are other features of thermostats. Thermoset polymers have the ability to be recycled and are better than thermosets in this respect, but due to their high cost, they cause many problems in manufacturing. High strain until the moment of failure, low moisture absorption and low resistance to solvents are other characteristics of thermoplastics. Although the use of thermoplastics is increasing nowadays, thermosets have good rigidity and have better performance at higher temperatures. On the other hand, remelting of thermosets is not possible due to their reticulation, while thermoplastics are not reticulated and are solids that melt, shape, and then cool. Extreme chemical and thermal stability is characteristic of oxides, carbides, nitrides, which form the basis of ceramic materials. Their most important application includes outer wall of spacecraft. Their working range is 2000 to 4000 degrees Fahrenheit and 6000 degrees Fahrenheit for one or two minutes.

1-2-3- Metals

     The most important materials of the metal background are aluminum, magnesium and copper. The first use of metal matrix composites was in space shuttle components. These materials are used as rims, pistons, turbine blades, etc. have been used.

1-3- Classification of reinforcements

1-3-1 Fibers

They are materials that, compared to other materials, have a very long axis and their strength in the longitudinal direction is much higher than in other directions.

1-3-2- Fibers Glass:

      Glass fibers are the most common types of fibers that have been used for centuries. In the Renaissance period, for strength, glass threads were connected to delicate and thin objects in a cross or braided form. Glass fibers are divided into four categories based on reinforcement for specific performance.