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Home / Issues / № 2, 2014

Engineering

MODELING OF NON-STATIONARY OF STRESS WAVES IN SOLID DEFORMABLE BODIES COMPLEX AREA
Musayev Vyacheslav Qadyr ogly

For solving boundary value problems finite element method is used for movement. The above problem is solved by the method of end-to-end account, without allocation of breaks (homogenous algorithm).

In [1-7] provides information on the mathematical modeling of stress waves in solid deformable bodies.

Using the finite element method the boundary value problem is replaced by a Cauchy problem. Next problem is solved using the Galerkin method. For approximation of the considered variables (space and time) used finite elements of the first order. For the main unknown at the nodal point taken two moves and two speeds of movement for a linear problem.

Using the Galerkin method, the system of linear ordinary differential equations of second order in the displacements with the initial conditions given by an explicit two-layer scheme.

A study of convergence and stability of finite element schemes. Research has shown that they satisfy the condition of stability Neumann.

For approximation of the investigated complex area, use the simple regular subdomains.

Proposed quasi-regulated approach to the solution of systems of linear ordinary differential equations of second order in the displacements with the initial conditions and to the approximation of the area of study. The method is based on the schemes: point, line, plane.

A comparison with the results of the analytical solution for the problem of the impact of a plane longitudinal elastic waves type of the Heaviside function to free a round hole. A comparison with the results of the numerical solution is 6%.

A comparison with experimental results obtained using the method of photo-elasticity, for the problem of the impact of a plane longitudinal elastic waves on a free round hole. A comparison with the results of the numerical solution is 2%.

A comparison with the results of the analytical solution for the problem of the impact of a plane longitudinal elastic waves type Heaviside function supported on a round hole. A comparison with the results of the numerical solution is 12%.

A comparison with numerical solutions obtained using the mixed finite element method in solving the problem of the impact of a plane longitudinal elastic waves type of bottom half-sine gravity dam normal profile (Kurpaska dam). A comparison with the results of the numerical solution is 5%.

We consider the problem of the impact of fundamental shocks (Delta function and the Heaviside) of the endless strip, and plate, as well as on the half-plane. The obtained stress components in the characteristic areas of the investigated tasks.

Studies of convergence and stability, compared with the results of other methods showed good agreement, which allows to make a conclusion about the physical validity of the results of the numerical solution of time-dependent wave problems.

The methods, algorithms, complex programs and results of the tasks are recommended for use in scientific and technical organizations specializing in the field of dynamic calculation of unique objects with the environment.

 



References:
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Bibliographic reference

Musayev Vyacheslav Qadyr ogly MODELING OF NON-STATIONARY OF STRESS WAVES IN SOLID DEFORMABLE BODIES COMPLEX AREA . International Journal Of Applied And Fundamental Research. – 2014. – № 2 –
URL: www.science-sd.com/457-24639 (21.08.2019).