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# loads or enforced displacements are not mandatory for nonlinear quasi-static solutions, if gap or contact elements are present in the model

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### Mohammed

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## Nonlinear Static Analysis

This solution sequence performs static nonlinear analysis. Static inherently implies that a process occurring in real-time is being simulated infinitely slowly.

## Nonlinear Static Analysis

This solution sequence performs static nonlinear analysis. Static inherently implies that a process occurring in real-time is being simulated infinitely slowly.

This allows the equilibrium equation to be satisfied at each step and inertia, momentum effects are ignored. Therefore, the possibly dynamic problem can be solved as a static problem (static).

## Nonlinearity Sources

### Geometric Nonlinearity

In analyses involving geometric nonlinearity, changes in geometry as the structure deforms are considered in formulating the constitutive and equilibrium equations. Many engineering applications require the use of large deformation analysis based on geometric nonlinearity. Applications such as metal forming, tire analysis, and medical device analysis. Small deformation analysis based on geometric nonlinearity is required for some applications, like analysis involving cables, arches and shells. Such applications involve small deformation, except finite displacement or rotation.

### Material Nonlinearity

Material nonlinearity involves the nonlinear behavior of a material based on current deformation, deformation history, rate of deformation, temperature, pressure, and so on.

### Constraint and Contact Nonlinearity

Constraint nonlinearity in a system can occur if kinematic constraints are present in the model. The kinematic degrees-of-freedom of a model can be constrained by imposing restrictions on its movement. In OptiStruct, constraints are enforced with Lagrange multipliers.

In the case of contact, the constraint condition is based on inequalities and such a constraint generally does not allow penetration between any two bodies in contact.

Applied loads can depend upon the deformation of the structure when large deformations are involved. Geometrically, the applied loads (Forces or Pressure) can deviate from their initial direction based on how the model deforms at the location of application of load. In OptiStruct, if the applied load is treated as follower load, the orientation and/or the integrated magnitude of the load will be updated with changing geometry throughout the analysis.

## Nonlinear Static Analysis Types

The following analysis types are available in the Static Analysis domain within OptiStruct to solve nonlinear models.

Small displacement analysis cannot handle all the nonlinearities specified in the previous section. In such cases, Large displacement analysis can be used. Currently, small displacement analysis is used by default and large displacement analysis can be activated (LGDISP), if required.

### Small Displacement Analysis

In small displacement analysis the sources of nonlinearity are restricted to contact, GAP elements, and MATS1 elastic-plastic material. Geometric nonlinearities, follower loads, and large strain elasto-plasticity cannot be handled by small displacement analysis. As a typical guideline, small displacement analysis should be limited to small strains (some 5 percent strain) in both translation and rotation. There is no update of gap/contact element locations or orientation due to the deformations. They remain the same throughout the nonlinear computations. The orientation may change, however, due to geometry changes in optimization runs.

### Large Displacement Analysis

Large Displacement Nonlinear Static Analysis (LGDISP) is used for the solution of problems wherein the load response relationship is nonlinear and large structural displacements are involved. The source of this nonlinearity can be attributed to multiple system properties, for example, materials, geometry, nonlinear loading and constraints. Currently, in OptiStruct the large displacement capabilities include large strain elasto-plasticity (MATS1), hyperelasticity of polynomial form (MATHE), contact with small tangential motion, deformation dependent loads (follower loads), and rigid body constraints.

## Nonlinear Solution Method

Nonlinear problems are generally history dependent. In order to achieve a certain level of accuracy, the solution must be obtained in a series of small increments.

For this purpose you need to solve the equilibrium equation at each increment and a corresponding increment size is selected. Newton's method is used to solve the nonlinear equilibrium equation in OptiStruct. If the solution is smooth, quadratic of rate of convergence may be achieved when compared with other methods. This method is also very robust in highly nonlinear situations.

Choosing a suitable time increment is very important. In OptiStruct, an automatic time increment control is available. It should be suitable for a wide range of nonlinear problems and, in general, is a very reliable approach. In future OptiStruct versions, additional user control options to set up automatic time increments may be provided.

The automatic time increment control functionality measures the difficulty of convergence at the current increment. If the calculated number of iterations is equal to optimal number of iterations for convergence, OptiStruct will proceed with the same increment size. If a lesser number of iterations is required to achieve convergence, the increment size will be increased for next increment. Similarly, if it is determined that too many iterations are required, the current increment will be attempted again with a smaller increment size.

स्रोत : 2021.help.altair.com

## Non linear quasi

Non linear quasi-static analysis using gap elements - Non linear quasi-static analysis using gap elements - Altair OptiStruct - Altair Products

## Non linear quasi-static analysis using gap elements - OptiStruct - Altair Products

Question

### Non linear quasi-static analysis using gap elements

by Altair Forum User Participant created 4y ago ago in Altair Products Hi all,

I was running a model in Optistruct 13.0 dealing with a two step non linear quasi-static analysis of two plates coming into contact. In the first step my goal is to make sure the two plates don't come into contact; let's say my initial gap is 5 mm, one plate is pushed down by a force of 100 N, the other one is fixed at the base. At the end of this step the two plates should have minimum gap between them, in other words no load should be transferred from one to another. After the second step in which I apply a force of 1000 N, the two plates obviously come into contact, resulting in a load transfer to the spcf applied at the base of the fixed plate, since friction between the plates is activated. I tried using a gap element in order to simulate the problem but no matter how I change the values into the pgap card (for example I first put a value of Kb equal to 25 N/mm to make sure the pushed plate didn't reach 5 mm of displacement with a force of 100 N.... didn't work, then I put it equal to 0 and I obtained the same result ), at the end of the first step the gap of 5 mm is always reached, resulting in load transfer. How can I avoid this situation in order to make it work properly? I'll attach the .hm file so you can check it. Thanks for any replies, hope someone will help me with this matter!

model_with_gap.hm Topics: OptiStruct Upvotes (0) 1276 Views

6 Replies T tinh

Collaborator • 4y ago

ago

Why don't you set initial distance as 0mm and then apply 1000N load? there was a similar example in hw solver help

Helpful (0) AFU Altair Forum User

Participant • 4y ago

ago HI @Dirk76

Do you mean something like this?

Helpful (0) AFU Altair Forum User

Participant • 4y ago

ago

On 6/18/2018 at 10:10 AM, Prakash Pagadala said:

HI @Dirk76

Do you mean something like this?

after the first iteration with 100 N, the two plates don't come in contact? then it's what I need, since everytime I apply different load values the two plates reach the initial gap.

If it's the case, would you share the model? Thanks.

On 6/18/2018 at 10:01 AM, tinh said:

Why don't you set initial distance as 0mm and then apply 1000N load? there was a similar example in hw solver help

that's because my main goal is to have the two plates in contact only after the second step of the analysis, so I need to set the problem in this way.

Helpful (0) AFU Altair Forum User

Participant • 4y ago

ago HI,

So you want the blocks to come in contact in 1st subcase and not in 2nd subcase?

Helpful (0) AFU Altair Forum User

Participant • 4y ago

ago

On 6/26/2018 at 1:11 PM, Prakash Pagadala said:

HI,

So you want the blocks to come in contact in 1st subcase and not in 2nd subcase?

My goal is to have them in contact during second subcase. If the initial gap is 5 mm and during the first subcase I apply 100 N, the two plates shouldn't come in contact... this is why there's some mistake in the model. If you try to increase the gap, with that contact (or different, I tried various solutions) formulation, no matter what, the plates will come into contact.

A model that work with these initial conditions should be made in a way that the gap only reduces of a finite quantity < initial gap, so that increasing the load in the following substeps the gap should reduce to 0.

When you tried running this model, you obtained these results?

Helpful (0) AFU Altair Forum User

Participant • 4y ago

ago Hi,

I will share the model files soon.

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स्रोत : community.altair.com

## Static, quasi

Read 10 answers by scientists to the question asked by Meshel Q Alkahtani on Apr 17, 2014

Question

Meshel Q Alkahtani

King Khalid University

## Static, quasi-static and dynamic properties: How is each category defined?

Please suggest examples and documents as to whether static and quasi-static properties can be applied successfully on an analytical and numerical study of dynamic or ballistic phenomena.

Mechanical Engineering

Dynamic Assessment Static Analysis Numerical Analysis

17th Apr, 2014 Scott Sibole

The University of Calgary

In a static problem we assume acceleration is zero. Therefore, the sum of all forces = mass*0 = 0 and mass can be ignored.

Quasi-static means that at a given instant in time we can assume the problem is static. This assumption works well when inertial effects are very low. The term is typically used for non-linear problems where we simplify the non-linear system of equations to a linear system at a small increment with something like Newton's method.

Dynamic means that accelerations are not zero, and we must consider mass (inertia), i.e. sum of all forces = m*a

Cite 26 Recommendations

20th May, 2021

Nikolay Goloshchapov

Independent Researcher

Thank you Davide! It is truth! Regards!

Cite

17th Apr, 2014 Scott Sibole

The University of Calgary

In a static problem we assume acceleration is zero. Therefore, the sum of all forces = mass*0 = 0 and mass can be ignored.

Quasi-static means that at a given instant in time we can assume the problem is static. This assumption works well when inertial effects are very low. The term is typically used for non-linear problems where we simplify the non-linear system of equations to a linear system at a small increment with something like Newton's method.

Dynamic means that accelerations are not zero, and we must consider mass (inertia), i.e. sum of all forces = m*a

There are another dynamic analysis which it is semi-dynamic method. This method usually is used in underground structure under dynamic loading such as earthquake. In the method you have to give the dynamic strain (Shear strain) to the numerical model and analyse it and after analysis you can design the structure elements.

There several emprical models to calculate the shear strain.

Cite 1 Recommendation 30th Sep, 2014 Scott Sibole

The University of Calgary

Hi Nhan,

Yes, that is exactly what I mean.  At every increment in the non-linear solution you are solving a static problem.

Best, Scott Cite 1 Recommendation 5th Apr, 2015 Reza Rezaei

University of Tehran

A static load is time independent. A dynamic load is time dependent and the inertial effects can not be ignored. A quasi-static load is time dependent too but is slow enough in a way that its inertial effects are negligible.

Cite 17 Recommendations 28th Aug, 2016

Nikolay Goloshchapov

Independent Researcher

Some researchers assume that quasi-static conditions of loading is when the vc it is hyper-sonic deformations and in this case all displacements of medium are out of field of limit of strength. The quasi-static state is the analogue of the static state, when the acting forces are not depend to speeds of loading or the duration of action of loading. Approximately we can take it when v<

Cite 6 Recommendations 4th Apr, 2018 Faheem Ur Rehman

University College London

In the applications, where multiple autonomous vehicles tow a mass is solved assuming quasi-static model. In this way, we solve the complex nonlinear model by assuming slow speeds.

Cite 1 Recommendation 29th Oct, 2018 Hussam Ali Mohammed

Al-Furat Al-Awsat Technical University

Meshel Q Alkahtani ...Please check references below.. hope it will be helpful for you…

Regards…

https://www.researchgate.net/post/The_differences_between_static_quasi-static_stress_analyses_and_dynamic_stress_analyses

Article Quasi-Static and Dynamic Properties of Ti-4Al-3V-0.6Fe-0.2O ...

Cite 1 Recommendation 17th Nov, 2020 Davide Banfi JBA Group Hi Meshel,

it mainly depends on both natural frequency of the structure and impact duration of the external force on the structure.

In particular, the distinction between dynamic and static analysis is typically evaluated on the basis of the acceleration of the applied action in comparison to the structure's natural frequency. When a load is applied sufficiently slowly, the inertia forces can be neglected and the analysis can be simplified as a static analysis. In contrast, when the structure is exposed to dynamic loads, its motion is characterised by rapid oscillations. Dynamic analyses are used to describe the time histories of the structural oscillations in terms of acceleration, velocity, displacement and their relative frequency response modes. Such oscillations depend on both the characteristics of the structure (natural frequencies and geometrical configuration) and the external wave load (temporal and spatial variation of the force). Further details can be found in the link below.

स्रोत : www.researchgate.net

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Mohammed 4 day ago

Guys, does anyone know the answer?