Questions tagged [numerical-methods]

Questions concerning problems which cannot be exactly solved, or where the exact solution may be much more difficult to acquire than a solution by numerical methods.

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Does Finite Element Method use direct stiffness method?

Does Finite Element Method use direct stiffness method? Or it is another mathematical method? We definitely use direct stiffness method to solve frames. FEM is based on entirely this or depending on ...
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1answer
42 views

Analytical solution of thermal stress in a bi-metallic cylinder

As a side project I have looked to solve using Python an analytical solution for one-dimensional transient heat transfer in a thick cylinder with cladding on the inside surface, wherein the fluid in ...
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33 views

Provide stability for a 3D object with a support structure

This is a follow-up to this question. I wonder if structural engineering tools like Finite Element etc. might help create such support structures. If so, how?
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42 views

ABAQUS UMAT SDVINI problem

I'm trying to write a UMAT code for unsaturated soil model and I need to define some state parameters. I found that I can do that by using SDVINI subordinate. Should I put it at the and of UMAT? How ...
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22 views

Water distribution through N x Needle orifices

Consider a water distribution setup consisting of a feeder line blocked at one end but having 100 needle outlets all the same size. The feeder line cross sectional area is much greater than a needle ...
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1answer
36 views

How to use the Ritz method with the weak form to approximate solution of differential equation

I am having trouble understanding how to approximate the solution to this problem using the Ritz method and the weak form: $$\frac{d^2u}{dx^2} - u=0; \ \ x \in [0,1]$$ $$u(x=0)=0; \ \ \frac{du}{dx} \...
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22 views

Defining appropriate test function spaces for the finite element solution of Euler's fluid equations

I have the following coupled equations for the conservation of mass and momentum of a compressible fluid \begin{equation} \rho_t + (\rho u)_z = 0, \end{equation} $$ (\rho u)_t + (\rho u^2)_z + \...
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14 views

MATLAB code implementing the Finite Difference solution of the BVP

I'm having a hard time refiguring this code we used in class to do a 1D finite-difference solution. If anyone could help it would be greatly appreciated. The problem set is listed below as well as the ...
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17 views

Transient Heat Transfer Problem for a parabolic PDE of Rectangular Plate

I was able to write the elliptic PDE for the steady-state temperature of the plate but I am having a very hard time doing the same for the transient problem. Now consider the transient problem for ...
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1answer
33 views

Negative Eigenvalues in Ritz Solution of First-Order Shear Deformation Theory

I am trying to write a MATLAb code for determining the natural frequencies of a first-order shear deformation plate using Ritz method. I am using Legendre polynomials as trial functions in Ritz method,...
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29 views

Simufact / MARC and Fortran

I am using Simufact from MSC Software to perform numerical simulations. To be able to create my own sub-routines I need to have Fortran compiler installed. Simufact manual mentions only Intel Fortran +...
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28 views

How to code this iterative scheme for solving 2-group diffusion equation?

I am trying to write a python code to solve the neutron diffusion equation to model neutron flux distribution in a one-dimensional two-group setting. The governing equations of the system are: $$-...
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32 views

Implicit and Explicit finite difference discretization of steady state heat conduction equation

I understand what an implicit and explicit form of finite-difference (FD) discretization for the transient heat conduction equation means. But I am not able to understand if it is possible to ...
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1answer
107 views

FEA: Newton-Raphson algorithm for Dirichlet BC non-linear static analysis

I have a standard non-linear static problem to solve with FEA. I am applying displacement boundary conditions only, no external force. The equation to solve look like these: $K(u)u=R(u)$ Eq(1) The ...
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1answer
69 views

Calculate surface area and outward normal of each face(non-planar) for a irregular hexahedron.

I am using the vector cross product to calculate each surface area and thus the outward normal. However, this approach fails when the surfaces are non-planar. So what is the best approach to calculate ...
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1answer
34 views

Temperature not changing in my code for 1-D heat equation: Explicit Scheme

I am trying to solve the following 1-D heat equation with provided boundary conditions using explicit scheme on Matlab. I have been trying to plot the results but I realized that my temperatures are ...
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2answers
1k views

Example of real-life problem solved with numerical methods? [closed]

I hope this is a suitable question to ask here. Well, I'm taking Numerical Methods this semester (also called 'Numerical Analysis' in some places). The term-assignment is to find a real-life problem ...
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33 views

How to formulate a 3D version of the Navier-Stokes equations in 2D for numerical solution?

I'm considering a topology optimization problem where the design domain is a rotating annulus (in $\mathbb{R}^2$). One of the adjoint equations of the Navier-Stokes system whose solution is to be used ...
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544 views

How does Abaqus calculate reaction force?

I wrote a UEL for one element and compared to a reference UEL (FEM), where the results agreed satisfactorily, except the reaction force. The stress, strain, strain energy all were pretty accurate. I ...
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37 views

Discretise this transport equation

I am trying to discretise the PDE: $$\phi \frac{\partial c}{\partial t}+\frac{\partial j}{\partial x}=0$$ where $c$ is a function of $x$ and $t$, and $j=qc-D(q)\frac{\partial c}{\partial x}$, $q$ is ...
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1answer
311 views

How to derive deformation gradient or displacement gradient?

In one of my project, I need deformation gradient or displacement gradient for some elements in my model that made by ABAQUS software and I can't find it directly, any suggestion or help would be ...
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1answer
52 views

Mechanical Engineering- Modeling contact in Abaqus

I have simulated a 2D model in Abaqus which indicates 2 main part, first a sector that represent as wheel and, second a rectangular that represent rail. the wheel and rail are in contact and wheel ...
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14 views

Does excitation matter in a time-domain simulation/computation of a transfer function of an LTI system?

Let's say I am running a FDTD simulation of a wave-equation to determine a transfer function of an LTI system: \begin{equation} H(f) = \dfrac{Y(f)}{X(f)}\ \end{equation} where $Y(f)$ and $X(f)$ are ...
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3answers
1k views

J2 orbit propagation problem in MATLAB (solver instability)

The problem is that when I try to solve the following equations of J2 perturbed gravity: ...
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0answers
2k views

How to calculate effective strain in plane stress?

What is the correct formula to calculate the effective strain under plane stress conditions? In plane stress it is assumed that the out of plane stresses are zero. The out of plane strains are not ...
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3answers
898 views

Deflection of thin plate with 1 free edge and deflection > thickness

I have an thin uniform rectangular steel plate supported on 3 sides and free on one, and supporting a uniform load. I'm trying to determine what thickness of plate I need to keep deflection below a ...
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2answers
2k views

Normalization and Non-Dimensionalization of a mass balance equation

I would like to ask what is the difference (if any) between normalization and non-dimensionalization. I will try to explain what I have done until now with an equation that I would like to work with ...
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59 views

Sliding mode surface derivative exact matrix format (ds/dx)

Is there any suggestion on sliding surface state derivative matrix (ds/dx) format? ...
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1answer
115 views

Sliding mode surface derivative using numerical method

In the article Controller Design using Bifurcation Map for Aircraft Spin Recovery, the sliding surface derivative is obtained using a numerical method. The steady space system is defined by the ...
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2answers
507 views

External diffusion: calculation of surface concentration

I am struggling a bit with an external diffusion problem. I am trying to calculate the concentration at the surface (as well as surface reaction rate) and would like some help or guidance. Here is ...
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43 views

Verify parameters variation in local sensitivity coefficients for microkinetic model

I’m performing a sensitivity analysis for a model of a set of elementary chemical reactions. I’m considering the variation in species concentration ($c_{k}$) with respect to the forward reaction rate ...
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1answer
363 views

Different calculations for values of thermodynamic properties

While deciding what tool (library) to use for a simulation of a hybrid gas turbine plant, I found that different libraries/tools of thermodynamic properties yield different values than the other. I ...
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2answers
810 views

How are thermodynamics properties of gases and liquids calculated numerically?

I was wondering how the values of thermodynamic properties as enthalpy, entropy, internal energy, specific heat, specific volumes ... etc, of gases and liquids are calculated using programming ...