why can the compliance and stiffness tensors for cubic and orthotropic materials be greatly simplified from the general case?

Answers

Answer 1

The compliance and stiffness tensors for cubic and orthotropic materials can be greatly simplified from the general case because these materials have specific symmetry properties that allow for certain components of the tensors to be equal to each other or even zero

For example, in cubic materials, all three axes have equal stiffness and compliance, so only one value needs to be specified for each. In orthotropic materials, there are three mutually perpendicular planes of symmetry, which greatly reduces the number of independent components in the tensors. This simplification makes it easier to model and analyze the mechanical behavior of these materials. The compliance and stiffness tensors for cubic and orthotropic materials can be greatly simplified from the general case because these materials exhibit symmetry in their properties. In both cubic and orthotropic materials, the mechanical properties are directionally dependent, but they follow specific patterns.For cubic materials, the properties are isotropic within the three mutually perpendicular planes, while in orthotropic materials, the properties are isotropic within each of the three orthogonal planes. This symmetry allows for a reduced number of independent constants, simplifying the tensors and making them easier to work with in engineering applications.

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Answer 2

The compliance and stiffness tensors for cubic and orthotropic materials can be greatly simplified from the general case due to the specific symmetries present in these materials.

Cubic and orthotropic materials have symmetry in their elastic properties, which allows for a reduction in the number of independent elastic constants. In the general case, anisotropic materials have 21 independent constants in their stiffness tensor. However, cubic materials have only 3 independent constants, while orthotropic materials have 9 independent constants.

This simplification arises because the symmetry of cubic and orthotropic materials leads to specific relationships between the elastic constants. These relationships reduce the complexity of the compliance and stiffness tensors, allowing for easier analysis and calculation of material properties.

In summary, the compliance and stiffness tensors for cubic and orthotropic materials can be greatly simplified from the general case due to the symmetry in their elastic properties, which reduces the number of independent elastic constants.

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Related Questions

Assume:

A = 1101 0011 1111 0110

B = 0110 1101 1101 1110

Write the series of operations necessary to pack A into B (and store the result in C), where the 8 lowest order bits of B are stored in the 8 highest order bits of C, and the 8 highest order bits of A are stored in the 8 lowest order bits of C.

Answers

To pack A into B and store the result in C, the following operations can be performed.

What is the explanation for the above response?

Perform a logical shift right on A by 8 bits, which will result in 0000 0000 1101 0011.Perform a logical shift left on B by 8 bits, which will result in 1011 0110 1101 1110.Perform a logical OR operation between the results of step 1 and step 2, which will result in 1011 0110 1111 1110.Perform a logical shift left on A by 8 bits, which will result in 0000 0000 0000 0000.Perform a logical shift right on B by 8 bits, which will result in 0000 0000 0110 1101.Perform a logical OR operation between the results of step 4 and step 5, which will result in 0000 0000 0110 1101.Perform a logical OR operation between the results of step 3 and step 6, which will result in C = 1011 0110 1111 1110 0000 0000 0110 1101.

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This manipulator is used to establish a field width for the value that follows it: field_width set field setw iomanip None of these

Answers

The manipulator used to establish a field width for the value that follows it is setw from the iomanip library in C++. It allows you to specify the number of characters that should be used for the output of the value.

For example, if you want to output a value with a field width of 5, you would use set w(5). This will ensure that the value is formatted with 5 characters, adding spaces as necessary to achieve the desired width. So the correct option in this case would be "set field setw iomanip". The term "set field set w iomanip" does not make sense in this context.
The manipulator used to establish a field width for the value that follows it is "setw". This term is part of the iomanip library in C++. So, the correct answer is "setw". The other terms mentioned in the question, such as "field_width", "set field", and "setw ioman ip", are not relevant to the context of the question.

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The manipulator in question is called "setw" and it is a part of the "iomanip" library in C++. option c is correct.

This manipulator is used to set the field width for the value that follows it. The value can be a string, integer, or any other data type.

The purpose of setw is to make the output more readable and organized by aligning the data in columns. For example, if you are printing a table with multiple columns, you can use setw to set the width of each column so that the data is aligned and easy to read.

The syntax for using setw is as follows:

cout << setw(10) << "Hello";

In this example, setw(10) sets the field width to 10 characters for the string "Hello". This means that "Hello" will be printed with a width of 10 characters, even if it is shorter than that. If the string is longer than 10 characters, it will be truncated to fit within the allotted space.

Overall, setw is a useful manipulator for formatting output in C++. It helps to make the output more readable and organized, which is important when dealing with large amounts of data.

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Note: The complete question would de as bellow,

This manipulator is used to establish a field width for the value that follows it:

a)field_width

b)set field

c)setw

d)iomanip

e)None of these

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