Wednesday, 18 September 2019

# Second Theorem of Castigliano,Computational Material Science

Second Theorem of Castigliano: Second Theorem of Castigliano is also known as Menabreas theorem which states that the forces developed in the redundant framework are such that the total elastic strain energy is minimum. In this article, I am going to explain what is the Second theorem of CASTIGLIANO and Computational Material Science in a detailed manner.

## Explanation of Second Theorem of Castigliano:

If F1, F2 & Fr are the forces in redundant members of the framework and ‘U’ is the elastic strain energy then

∂U/∂F1=0,∂U/∂F2=0…………………………………………………………………………………………………………∂U/∂Fr=0

This is also called a Principle of least work.

To explain about the Second Theorem of Castigliano, we can consider two structures

• Redundant Structure
• Structure with redundant members removed

The detailed explanation of the Second Theorem of Castigliano is shown below in the form of written material.

The detailed explanation of the Second Theorem of CASTIGLIANO is shown below in the video which is in the form of written material.

This is the complete explanation of the Second Theorem of CASTIGLIANO which is shown in a detailed manner. If you have any doubts, feel free to ask from the comments section. Please Share and Like this blog with the whole world so that it can reach to many.

The Other concept that I was discussing is the Computational Material Science which has the role, Aim, Goal and Scope of Computational Material Science and was discussed below.

Computational Material Science:

Computational Material Science is associated with their design, synthesis, processing, characterization, and utilization. It also helps to report on results that provide new insights into materials. This post focuses mainly on the history, Role, Aim, Goal and Scope of Computational Material Science and its expansion.

History of Computational Material Science:

The first case study of materials that used digital computers was made shortly after the 2nd world war. The Legendary Mathematician “John Von Neumann” at wartime in Los Alamos National Laboratory credited as being the first to seriously consider Numerical Methods and encourage using computing machines.

Research:

One of the focus of research at that time was on “How irradiation of high energy particles would change a material’s structure and properties”?

Because of less availability of digital computers, the work was not faster. But now, MS is an active and fast-growing field. As its impact has grown, it has gained a reputation as being the third approach for scientific research and engineering, parallel to experimentation and theory.

• Compared to humans, computers are more efficient and less error-prone in handling repetitive or numerical tasks. For this reason, computers are used extensively in materials research to do tedious work such as “data acquisition and data analysis”.

The role, Aim, Goal and Scope of Computational Material Science:

Role:

Computational Material Science plays a fundamental role in the

• Development
• Planning
• Manufacturing of new materials
• Processes and devices

Aim:

To understand and predict the structures-Properties, relationships of materials in various length scales, from not only the continuum(‘mm’ and Up)level but also from the mesoscopic(microns) and Atomic (Nm & Angstroms) levels.

Goal:

• To report on results that provide new insights into materials
• Significantly expand our understanding of the properties of materials
• Phenomena associated with their design, synthesis, processing, characterization, and utilization.

Scope:

Computational Material Science focuses on the development of

• Computational methods
• Numerical Techniques
• Theories and Algorithm which are used by the material science community

### You can also know about:

This is the complete explanation of Computational Material Science which is shown in a detailed manner. If you have any doubts, feel free to ask from the comments section. Please Share and Like this blog with the whole world so that it can reach to many.

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