The Interconnectivity of Theoretical, Material, and Structural Mechanics

Theoretical mechanics, material mechanics and structural mechanics are collectively referred to as “engineering mechanics”, which are the three major disciplines in the mechanics foundation of engineering.

The research content of theoretical mechanics includes statics, kinematics and dynamics.

There are many contents that are identical with the mechanics part in Physics, and of course there are also deepening contents.

In the engineering discipline, especially in architectural structure design, the statics part is used more.

In fact, kinematics is a very important content in mechanical engineering and aerospace engineering.

Taking mechanical engineering as an example, the design of a mechanism needs to first analyze its motion state, calculate the velocity and acceleration of each component, and then carry out force analysis with the help of dynamic equations, of course, statics knowledge is indispensable.

The same is true in fluid mechanics.

Taking the calculation of the elbow anchor block of pressure pipeline as an example, when analyzing its stress state, the momentum equation in dynamics needs to be used to calculate the impact force of water.

Therefore, in the building structure, its statics part is relatively more applied.

The quasi-static method in the dynamic calculation (such as the method based on the response spectrum theory in the seismic calculation) is actually derived from the d’Alembert principle in theoretical mechanics (also called the dynamic static method, which is to transform the dynamic problem into a static problem to deal with it).

It can be said that theoretical mechanics is the basis of the discipline group of mechanics.

In material mechanics, structural mechanics, and even elastoplastic mechanics, the balance relationship of forces is involved, which is the content of statics research.

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The mechanics of materials studies the stress and deformation of bars.

The basic deformation includes axial tension and compression, shear, torsion and bending.

More complex deformation is nothing more than the combination of these basic deformation (for example, the stability of the compression bar is the combination of bending and axial compression).

The corresponding internal forces include axial force, shear, torque and bending moment.

From the microscopic point of view, the basic deformation can be attributed to normal strain and shear strain, the basic internal force can be attributed to normal stress and shear stress, and the bridge connecting stress and strain is Hooke’s Law.

From a macro point of view, the research method of material mechanics is to take an isolator and then study the balance relationship of forces.

Three basic equations are used: static balance equation, geometric equation and physical equation.

The static equilibrium equation is the content of statics in theoretical mechanics;

Geometric equation is a measure of the spatial relationship between the basic dimensions of a deformed bar;

The physical equation, also known as the constitutive equation, describes the relationship between stress and strain, that is, Hooke’s law (when considering complex stress states, it is also the generalized Hooke’s law).

Of course, several basic assumptions are required in the above research process: linear elasticity, continuous homogeneity, isotropy and small deformation.

If it exceeds a certain limit, it will produce a large error. At this time, elastoplastic mechanics and fracture damage mechanics should be used for research.

In the mechanics of materials, we will also study some geometric properties of cross sections: area, static moment, moment of inertia, product of inertia, polar moment of inertia, radius of inertia, etc.

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Since it is a geometric property, it is purely a mathematical problem.

In fact, it is mostly calculated by the integral method.

There is no great difficulty here, but the calculation of composite sections is a little cumbersome.

Structural mechanics studies the force and deformation of bar structures, and studies concrete and practical structures, such as frames, bent frames, arches, trusses, etc.

The linkage structure is composed of members, which can be disassembled into members.

Therefore, the basis of structural mechanics is material mechanics, because in the final analysis, its basic deformation and internal force are completely the same as those studied in material mechanics.

Because of the member system, there are different research methods.

The basic methods are force method and displacement method.

From the perspective of practicality, some iterative methods are derived, such as moment distribution method, shear force distribution method, bending point method and D-value method in frame structure analysis, elastic center method in arch structure analysis, etc.

After further discretization, it is the matrix displacement method, which is further extended and extended to the widely used finite element method.

Only one is only applicable to the member structure (also known as “finite element analysis of member structure”), and the other is more applicable to continuous media (including solids and fluids), so its scope of application is wider.

Therefore, the development of mechanics is from simple to deep, from easy to difficult, and from simple to complex step by step.

Without theoretical mechanics as the basis, it is impossible to analyze the mechanical balance relationship of the structure and calculate the support reaction and structural internal force.

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Without material mechanics as the bedding, it is impossible to analyze the internal force and deformation of the structure.

Therefore, it is difficult to say which is more important, but a gradual process.

The study of mechanics is comparable to the study of mathematics.

The study of elementary mathematics can not be ignored because higher mathematics has a wider application range, deeper problem-solving, and sometimes even more concise.

Because some basic operation rules in mathematics (such as the law of combination, the law of exchange, the law of distribution, etc.) are generally applicable to higher and elementary mathematics.

And it is based on the summary of the operation rules of elementary mathematics (of course, there are also cases in higher mathematics such as not applying the exchange law, which is a major difference from elementary mathematics).

Therefore, the inheritance and expansion of a discipline is the basic internal law in the development of a discipline, and is also an important symbol of its continuous maturity and perfection.

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