# Simulation Bridge Dynamic Self-Weight Stress Analysis

Here we present a simulation of a bridge considering a dynamic self-weight stress analysis. The bridge in this article is modelled as a linear elastic material and Hooke's law is valid. The computation starts with an initial geometry created within the CAD software. Due to its self-weight the bridge starts to deform. Because the deformations are large, the motion and the acceleration of the bridge cannot be neglected in comparison infinitesimal strain theory. So, Newton laws are valid here and the force applied to a body produces a proportional acceleration and a time dependent consideration is required, of course.

Even though we used a linear elastic material in this case study, NOGRID software can compute viscoelastic materials as well. Unlike purely elastic bodies, a viscoelastic material has an elastic component and a viscous component. The viscosity of a viscoelastic material gives the body a strain rate dependence on time. Purely elastic materials do not dissipate energy when a load is applied and then removed. However, a viscoelastic material dissipates energy when a load is applied and then removed. Viscoelastic behavior has elastic and viscous components modeled as linear combinations of springs and dashpots, respectively. Each model differs in the arrangement of these elements. The elastic components can be modeled as springs of elastic constant E, given the formula:

σ = E ε

where σ is the stress, E is the elastic modulus of the material, and ε is the strain that occurs under the given stress, similar to Hooke's law. The viscous components can be modeled as dashpots such that the stress–strain rate relationship can be given as,

σ = η dε/dt

where σ is the stress, η is the viscosity of the material, and dε/dt is the time derivative of strain.

Figure 1: CAD groups created in NOGRID's COMPASS

Figure 2: Setup the bridge stress analysis case

Figure 3: Result view of the bridge stress case within NOGRID points' GUI

Figure 4: Animation displacement by self-weight load

The implemented Maxwell model can be represented by a purely viscous damper and a purely elastic spring connected in series. Under this model, if the material is put under a constant strain, the stresses gradually relax. When a material is put under a constant stress, the strain has two components. First, an elastic component occurs instantaneously, corresponding to the spring, and relaxes immediately upon release of the stress. The second is a viscous component that grows with time as long as the stress is applied.

The implemented Kelvin–Voigt model consists of a Newtonian damper and Hookean elastic spring connected in parallel. This model represents a solid undergoing reversible, viscoelastic strain. Upon application of a constant stress, the material deforms at a decreasing rate, asymptotically approaching the steady-state strain. When the stress is released, the material gradually relaxes to its undeformed state. Without viscous stress (η=0), the material is fully elastic, and only Hooke's law is valid.

In addition, the Generalized Maxwell model, also known as the Wiechert model, is implemented as well and it is the most general form of the linear model for viscoelasticity. It takes into account that the relaxation does not occur at a single time, but at a distribution of times. The Generalized Maxwell model consists of one or more Maxwell elements (viscous damper and elastic spring connected in series), an optional pure viscous and an optional pure elastic element, all assembled in parallel. One special deduction of the Generalized Maxwell model implemented in NOGRID software is the Tool-Narayanaswamy-Moynihan model.

NOGRID points can be used for designing and problem solving for all kinds of stress related tasks. NOGRID unites abilities to handle stress computations for large deformations and for a lot of viscoelastic materials and allows the simulation of any conceivable geometry and operation modes such as

• computation is in full 3D solving viscoelastic material behavior
• easy and intuitive setup
• free definable material properties by User equations or User curves
• Structure-Structure Interaction with viscoelastic materials
• Fluid-Structure Interaction using all viscoelastic models implemented
• computation of moving parts or moving boundaries in combination with viscoelastic materials

## Nogrid's strengths

Particular strengths of NOGRID's fluid flow CFD software are the rapid preprocessing (no fluid grid needs to be generated, only the boundary mesh, inner finite points are generated automatically depending on User setting initially and during computation), and the outstandingly short computation time even for complicated cavities.
As you can see in the image below, the boundary of the geometry still requires a mesh to allow the interior finite points to detect the boundary. The boundary must therefore be meshed and the finite points inside are automatically generated during the simulation controlled by User specifications.

## What is CFD from NOGRID?

CFD solves the fundamental equations that define the fluid flow process. With CFD software from NOGRID every engineer makes better decisions by predicting, analyzing and controlling fluid flow, heat and mass transfer or chemical reaction. By using NOGRID software for flow modeling you receive information on essential flow characteristics as for example flow distribution. Using it additional to testing and experimentation NOGRID software helps to improve the evaluation of your design – resulting in better construction and operation parameters, increasing planning security and money savings due to faster time to the marketplace for your product or process.

## Choose NOGRID

With NOGRID, you choose professional CFD software and services – our aim is helping you to be successful. When you decide to work with NOGRID you choose close cooperation with a dynamic, flat hierarchies-organization. Short information channels result in quick and accurate professional support and service. Our team consists of highly qualified employees, who are experts in fields such as numerical simulation or computational fluid dynamics. Based on our know-how, we are pleased to offer the following services, responding to your individual requirements:

## TRAINING

In our two-days training courses you will learn, how to use NOGRID CFD software efficiently. Our technical support team will teach you how to handle and solve different cases.

For more details please refer to Training Courses →

## Technical Support

We offer full professional support from the minute you start using our software, by telephone or by email. Contact us, when ever needed.

For more details please refer to Software Support

## Service

Lack of time or resources and other constraints often make outsourcing an attractive solution. We help you with your flow modeling needs. Based on our engineering expertise in this field we offer individual numerical simulation services matching the unique needs of your organization.

For more details please refer to Simulation Services →

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