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Because, when the nonlinearities are permitted, solution times will be much longer, and much more computational sources required. Understanding the natural or forced frequencies of the system is very important for healthy transient structural solutions. At these critical responses, part or system will respond to external excitements.

So, the application of time steps according to these critical frequencies can be very useful for transient structural analyses. And you can change the properties of existing material also. You need to have a geometry that has. You can select the parts one by one as shown by the red arrow above. Click on parts and define;. For transient analyses, you need to increase the mesh density on the regions of your physical model where;.

Also, you need to define proper contacts between various parts that constitute the whole assembly. Step controls are a very useful thing to optimize the loads and boundary conditions on parts of transient structural analysis. As we stated above, loads and boundary conditions are time-dependent in transient analyses. So, you will provide this time-dependent nature of loads and conditions by using time steps in transient structural analyses.

You can define pressures, forces, moments, loads, etc.. You can select; maximum tensile stress, maximum shear stress, mohr-coulomb stress, and others. Transient structural analysis is a very important tool for designers that are designing dynamic structural systems. NOTE: All the screenshots and images are used for educational and informative purposes. Your email address will not be published. Save my name, email, and website in this browser for the next time I comment.

Then, the program computes the two unknowns and by using the following equations:. The most important factors in choosing an appropriate time integration scheme for the finite element semi-discrete equation of motion given in Equation 15—5 are accuracy, stability, and dissipation. In conditionally stable time integration algorithms, stability is affected by a chosen size of the time step; whereas in unconditionally stable time integration algorithms, a time step size can be chosen independent of stability considerations.

In the Newmark method, the amount of numerical algorithm dissipation can be controlled by one of Newmark's parameters, , as follows:. With the Newmark parameters satisfying the above conditions, the Newmark family of methods may be unconditionally stable Hughes [].

By introducing the amplitude decay factor , the above conditions can be written:. Consequently, the program provides the user with the Newmark integration procedure, which is unconditionally stable via input of the amplitude decay factor on the TINTP command.

In the Newmark method, the amount of numerical dissipation can be controlled by one parameter in Equation 15—13 or in Equation 15— However, in low frequency modes the Newmark method fails to retain the second-order accuracy as. Note that the Newmark implicit method constant average method; namely, and , which is unconditionally stable and second-order accurate, has no numerical damping.

If other sources of numerical damping are not introduced, the lack of numerical damping can be undesirable so that the higher frequencies of the structure can produce unacceptable levels of numerical noise Hughes []. To circumvent the drawbacks of the Newmark family of methods, the program implements the generalized HHT- method which sufficiently damps out spurious high-frequency response via introducing controllable numerical dissipation in higher frequency modes, while maintaining the second-order accuracy.

To solve for the three unknowns , , and , along with Equation 15—8 and Equation 15—9 the generalized HHT- method uses the algebraic equation:. Equation 15—15 give the finite difference form:. Analogous to the Newmark method, the generalized HHT- method calculates the unknown at time by making use of Equation 15— Then, the program computes the two unknowns and by using the equations given in Equation 15—11 and Equation 15— Since the generalized HHT- method is also an implicit time scheme, the structural stiffness matrix must be factorized to solve for at time.

As mentioned in the literature Chung and Hulbert [] , the generalized HHT- method is unconditionally stable and second-order accurate if the parameters meet the following conditions:. By introducing the amplitude decay factor , the program also allows the user to control the amount of numerical damping if the four parameters on the TINTP command meet the following conditions:. If the WBZ- method is desired, the user can control the amount of numerical damping if the four parameters on the TINTP command meet the following conditions:.

Finally, the program also allows a user who wants to use the generalized HHT- method to control the amount of numerical damping if the four parameters on the TINTP command meet the following conditions:. It should be noted that the generalized HHT- method is second-order accurate and unconditionally stable.

This method allows you to control the amount of numerical damping. The amplitude decay factor is recommended to be set as Hughes [] , with which any spurious participation of the higher modes can be damped out and the lower modes are not affected. A significant amount of numerical damping may be introduced by setting , but it is not recommended.

In nonlinear structural dynamics problems, the internal load is no longer linearly proportional to the nodal displacement, and the structural stiffness matrix is dependent on the current displacement. Therefore, Instead of Equation 15—6 , any time integration scheme should be applied to the nonlinear semi-discrete equation:.

Equation 15—21 represents a nonlinear system of simultaneous algebraic equations; hence, any time integration operator may be used in association with the Newton-Raphson iterative algorithm. For nonlinear structural dynamics problems, both the Newmark method and the generalized HHT- method are incorporated in the program. The Newmark method assumes that at the time , the semi-discrete equation of motion given in Equation 15—21 can be rewritten as:. Note that is dependent on the current displacement at time.

In addition to Equation 15—22 , the Newmark family of time integration algorithms requires the displacement and velocity to be updated as given in Equation 15—8 and Equation 15—9. By introducing the residual vector , Equation 15—22 can be written as:. It is important to note that the time integration operator given in either Equation 15—22 or Equation 15—23 represents a nonlinear system of simultaneous algebraic equations. Therefore, a linearized form of the time integration operator can be obtained by the Newton-Raphson method as follows:.

Equation 15—24 gives:. For nonlinear structural dynamics problems, the program allows a user to input the amplitude decay factor or the Newmark integration parameters on the TINTP command. The generalized HHT- method for nonlinear structural dynamics problems assumes:. By introducing the residual vector , Equation 15—26 can be written as:.

The time integration operator given in Equation 15—26 or Equation 15—27 also represents a nonlinear system of simultaneous algebraic equations. Equation 15—28 gives:. Each are described subsequently. Only the full solution method is available for HHT Equation 15— In a nonlinear analysis, the Newton-Raphson method Newton-Raphson Procedure is employed along with the Newmark assumptions.

Automatic Time Stepping discusses the procedure for the program to automatically determine the time step size required for each time step. Inherent to the Newmark method is that the values of , , and at the start of the transient must be known. Nonzero initial conditions are input either directly with the IC commands or by performing a static analysis load step or load steps prior to the start of the transient itself.

This implies. The initial conditions are outlined in the subsequent paragraphs. Cases referring to "no previous load step" mean that the first load step is transient. If the previous load step was run as a static analysis TIMINT ,OFF , initial velocities are calculated using the previous two displacements and the previous time increment. Using either a single substep NSUBST ,1 or ramped loading KBC ,0 within the previous load step will result in nonzero initial velocities assuming nonzero displacement , as shown in Figure Figure The acceleration of a typical DOF is given by Equation 15—12 for time.

By default, the acceleration vector is the average acceleration between time and time , since the Newmark assumptions Equation 15—8 and Equation 15—9 assume the average acceleration represents the true acceleration. The velocity of a typical DOF is given by Equation 15— The static load is part of the element output computed in the same way as in a static analysis Solving for Unknowns and Reactions. The nodal reaction loads are computed as the negative of the sum of all three types of loads inertia, damping, and static over all elements connected to a given fixed displacement node.

This solution method imposes the following additional assumptions and restrictions:. Constant and matrices. A gap condition is permitted.

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