﻿ Solver improvements

# Solver improvements

2011.1

Recently, a new service pack of SCIA Engineer 2011 (internally called: SCIA Engineer 2011.1) was released on the market. This version was not announced as a big release, but nevertheless there are several very nice improvements done.

This producttip explains the improvements and new options related to the solver.

## Detailed Technical information

### Calculation protocol without time parameter

New setting in Solver setup:

If option is active:

if option is not active:

### Run one nonlinear combination ...

A new option has been added to the solver dialogue: Run one nonlinear combination:

When selecting this option the user can choose which nonlinear combination needs to be calculated:

##### Limitations:
• Only for Nonlinear combinations
• Not useful in case of Batch calculation
• Not useful in case of Steel code check (result of the limitation for Batch calculation)

The main goal of this solution is to reduce calculation time in case the user only wants to check one combination.

The difference in calculation time is shown in the example below.

### Example: Acces Chateau d'eau (scaffolding)

No. of nodes: 282

No. of beams: 436

No. of slabs: 21

No. of combinations: 42 Nonlinear ELU combinations 11 Nonlinear ELU combinations

Calculation time 1 NonLinear combination: 25 sec (this time includes also the selection of nonlinear combination)

Calculation time all Nonlinear combinations: 6min25sec

### Lanczos

The Lanczos method is a method to calculate the eigen values of a structure.

Lanczos is generally faster than the subspace iteration. As a result of tests, for very large systems (millions of unknowns), the Lanczos is at least two, or three times faster than the subspace iterations.

Only for extremely large projects it is necessary to use the pure iterative solver (SOLVER=ITERATIVE), which does not need the decomposition of the matrix. So Lanczos becomes the standard eigenvalue solver for 99% of applications.

The speed depends on the type of structure and numbers of eigenvalues demanded. Both, the subspace iteration method and the Lanczos, need the decompositon of the left hand side equations matrix. SCIA Engineer uses exactly the same procedure for both methods. This decomposition is done only once. The time of the first part depends on the number of unknowns and the bandwidth (more exactly: the space needed to store the matrix after decomposition) and it does not depend on the number of eigenvalues.

In the second part, there are the iterations, and in this part Lanczos is much faster, more than 3 times. The time of the second part depends on the number of equations and the number of eigenvalues and not on the bandwidth. This means that a larger speed for 2D (cca 3 times) and shell (cca 2 times) elements will be noticed, than for entire buildings, where the bandwidth is big. Next to this, a higher time difference between Subspace iteration and Lanczos is obtained for more eigenvalues. So, for structures with a small bandwidth and big number of eigen values (2D) the increase of speed will be more noticeable.

##### Comparision examples between the different eigen value calculation methods:

1. Customer project: (SNC Lavalin):

More details and project:

2. 12500 1D elements 3. 2D plate 4. Curved shell 5. Test example Ivan Beles

6. Test example FemCo

The structure is a square plate clamped on one side. 200 eigenvalues are solved. Conclusion: the Lanczos method is 2.96 times faster for 10000 FE and 3,59 times faster for 40000 elements than the subspace iteration.

For more theoretical background, look here: http://en.wikipedia.org/wiki/Lanczos_algorithm

### 3rd order analysis of Picard

Part of module: esa.10 - Geometrical nonlinearity.

The 3rd order method has following new possibilities:

• The Picard method
• The combination of the Picard and the Newton-Raphson method

With regards to the nonlinear calculations, there does not exist an universal and robust method. Generally the Newton-Raphson method is the best and will be used for majority of applications. Only when the method fails, a user can try either the Picard method, or the dynamic relaxation method. Both are generaly slower, but can help in cases, where the Newton-Raphson fails.

##### Summarized, the different analysis methods:
• Geometrical linearity: 1st order method
• Timoshenko: 2nd order with constant normal force
• Picard: 3rd order method
• Newton Raphson and Modified Newton-Raphson: 3rd order method
• Dynamic relaxation: 3rd order method
##### Application of the methods:

1st order (geometrical linearity):

• Concrete or brick buildings
• In general all structures where the first order (geometrical linearity) method is sufficient, i.e. small rotation (cca 2 degree) and much smaller loading (let`s say 10 times) than the critical load.

2nd order (Timoshenko):

• Standard steel halls
• In general all structures where the 1st order method (geometrical linearity) is not sufficient. Changes of normal or membrane forces in comparison to the linear solution are small. Also rotations are small (i.e. to 5 degrees)

3rd order: large displacements, large rotations, cables, membranes.

The following methods for the 3rd order are at disposal:

• Newton-Raphson (NR):
• Cables
• Shells
• Membranes
• In general all structures which cannot be solved by the 2nd order method.This method is the recommended method for the 3rd order calculations. Only if certain problems in convergence or singularities occur, it is recommended to try another method.
• Modified NR: to overcome singularity and/or to find a stable postcritical state. Could be also called "postcritical analysisâ€œ.
• Picard: can be stable in some cases where NR fails, but in most cases it is more time consuming than NR.
• Combination of Picard and NR: can be used to overcome the initial problem in NR. This procedure starts with the Picard method, to avoid possible problems in NR and then will switch to NR to obtain faster the equilirium state.
• Dynamic relaxation: more time consuming, but there will be no singularity problems.This method can be used for cables or membranes, or in some cases of material nonlinearity.

Astrid Bastiaens

03/06/2012