EffWidth ver. 01.2019 - Effective width calculation for the uniformly compressed simply supported plate

Author: Mihai Nedelcu, Technical University of Cluj-Napoca

You also need to install the MATLAB Compiler Runtime ver.9.5 (MCR).

EffWidth is a freeware program written in MATLAB R2018b that performs Geometrically Nonlinear Analysis with Imperfections (GNIA) in elastic domain for the uniformly compressed simply supported plate presented here. The plate edges parallel to y are constrained to identical movement in x direction.

The analysis is based on a new trigonometric series approach developed by the author and presented in a future paper.

Program interface

1^st application:

Input data:

h – plate thickness

w_{0_max}– amplitude of the initial geometric imperfection:

E – Young’s modulus

mu – Poisson’s ratio

f_y– material yield stress

L_y – plate width

L_x/L_y – length over width ratio (to be entered in the range (1, 1.414))

scale – scaling factor for the initial geometry and the deformed shape at 1^st yield

Output data:

· slenderness parameter (for the time being EffWidth is limited to values less than 10).

· Effective width at 1^st yield - the maximum value of the von Mises stresses in the mid-thickness plane is reaching the material yield stress f_y. At this stage the maximum displacement in z direction (w_max) and the compression load P are also provided.

· Effective width at maximum load (failure) is also provided. EffWidth is performing elastic GNIA, so the post-1^st yield strength reserve is approximated based on a separate shell FE study on square plates (see the future paper). Since a limited number of parameters were considered in this study, the calculation of the effective width at maximum load may be further optimized.

· Effective width given by the Eurocode semi-empirical approach (the optimised Winter’s formula).

· The difference between the Eurocode and the Eddwidth values for the effective width at maximum load.

· The deformed shape at 1^st yield.

· The map of von Mises, σ_x, σ_y, τ_xy stresses at 1^st yield.

2^nd application:

For this analysis you need to install Abaqus.

In order to validate the results, this application generates an Input file (*.inp) for Abaqus and launches the execution. The measuring units are [N, mm]. The initial load is P = 1000 N.

Input data:

The user must choose the folder where the Abaqus files are created, introduce the model name and the following parameters:

· considering the arc length increments: the maximum number, the initial, the minimum and maximum increment. The total arc length scale factor is set to 1.

· the maximum w displacement in the center of the plate, typically set as twice the maximum w displacement (w_max) found previously at 1^st yield.

· the shell Finite Element size. The Finite Element type is S4.

The application will inform the user when the analysis is finished. You can open the .odb file in Abaqus/CAE and check the results, typically the Load Proportionality Factor (LPF) curve and the LPF value when the von Mises stress equals the material yield stress, and the maximum load from which the effective width is calculated.