Finite Element Analysis: Concepts and Applications

Iso-parametric, Sub-parametric, and Super-parametric Elements

Iso-parametric Elements

In iso-parametric elements, the geometry and field variables (such as displacement and temperature) are interpolated using the same shape functions. The number of nodes used for defining the geometry is the same as that used for interpolating the field variables.

Example: A 4-node quadrilateral element where both geometry and field variables are interpolated with the same bilinear shape functions.

Sub-parametric Elements

In

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Spain’s Second Republic: Politics, Reforms, and Downfall

The Second Spanish Republic (1931-1936)

The Proclamation of the Republic and the Constitutional Period

The Elections and the Provisional Government

On April 12, 1931, municipal elections were held in Spain by universal male suffrage. The Socialists won the Republican nomination. On the morning of April 14, local councilors of Eibar, Gipuzkoa proclaimed the Republic, and throughout the day, the councilors of Valencia, Sevilla, Oviedo, Zaragoza, Barcelona, etc. followed suit. King Alfonso XIII fled the

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Augustine of Hippo: Life, Works, and Influence

Augustine of Hippo: Life and Works

Augustine of Hippo was born in Tagaste in 354 AD. His father was a pagan, and his mother was a Christian who taught her son, Augustine. He ceased to be a Christian, but then again, he did not embrace the Christian faith. He was always leaving the Christian faith. He went to Carthage to study rhetoric, read the work of Cicero, *Hortensius*, and became interested in the philosophical problem of evil, thus becoming a Manichean. Manichaeism was based on a Platonic way

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The Russian Revolutions of 1917 and the Rise of the Soviet Union

The February Revolution of 1917

The First World War exposed the weaknesses of the Russian Empire. During the war, the Russian Empire was in a situation that caused a considerable increase in prices and a lowering of the purchasing power of employees. This increased poverty among the population, both in rural and urban areas. Troops were poorly equipped and poorly directed. In late February, a strike erupted spontaneously in Petrograd (St. Petersburg), demanding food. The Tsar ordered the army to

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Spanish Colonization of the Americas: 15th-17th Centuries

**The Discovery of America: Late 15th Century**

The discovery of America cannot be studied without being framed in the cultural atmosphere and European economic framework of the 15th century. There are a number of factors that promoted the Atlantic momentum, including:

  • The need for new trade routes with India to break the traditional land routes and the Muslim geopolitical situation. This meant circumnavigating Africa to reach Asia or following the path of the sun.
  • A new scientific spirit that moved
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Financial Structure, Profitability, and Solvency Analysis

Item 8: Financial Structure and Analysis of Balances

Profitability Analysis

The profitability of an investment measures the relationship between the benefit and the resources used to obtain such a benefit. There are two types of profitability: economic and financial.

RE = Return on Equity

RF = Return on Assets

RE = Profit / Assets

RF = (Profit – Interest on Debts) / Equity

The company’s goal is to maximize performance for its owners. The most attractive profitability for investors is the financial return,

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Economic Growth and Development: Impact on Society and Environment

Economic Growth and Development

Unit 12: Economic Growth and Development

Economic growth refers to the continued increase in a country’s real output. When a country’s actual production increases, it raises the level of employment and income of its citizens, therefore increasing consumption. The state collects more taxes, which will raise revenue and increase public spending. The variables used to measure economic growth are real GDP and real GDP per capita.

Development occurs when there are a number

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Marxism, Women’s Rights, and Cold War Conflicts

Marxism (Scientific Socialism)

Karl Marx and Friedrich Engels published the works: The Communist Manifesto (1848) and Das Kapital (1867). Marxist theory is based on three foundations:

  1. Analysis of the past: The class struggle (oppressed against oppressors) is the engine of history.
  2. Review of the present: It analyzes the operation of the capitalist system, exploitation, injustice (surplus), and a tendency toward concentration of capital (stronger companies will absorb smaller ones), leading to an inevitable
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The Communist Manifesto: Historical Context and Impact

Origins in the Communist League

The Communist Manifesto originated from a commission given to Marx and Engels in December 1847 by the “Communist League.” Their task was to clearly and comprehensively articulate the ideological principles upon which the proletariat should base their struggle against the bourgeoisie. The Manifesto was published in February 1848, coinciding with the widespread outbreak of revolutions across Europe. While the work initially went relatively unnoticed amidst the turbulent

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Bengal School of Art: Impact on Modern Indian Painting

The Bengal School of Art

The Bengal School of Art, commonly referred to as the Bengal School, was an art movement and a style of Indian painting that originated in Bengal, primarily Calcutta and Shantiniketan. It flourished throughout the Indian subcontinent during the British Raj in the early 20th century.

Also known as the ‘Indian style of painting’ in its early days, it was associated with Indian nationalism (swadeshi) and led by Abanindranath Tagore (1871-1951). It was also promoted and supported

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