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1

ANN constitutive material model in the shakedown analysis of an aluminum structure

Potrzeszcz-Sut B., Pabisek E.

Computer Assisted Methods in Engineering and Science

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2014

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Vol. 21, no. 1

49--58

EN

The paper presents the application of artificial neural networks (ANN) for description of the Ramberg-Osgood (RO) material model, representing the nonlinear strain-stress relationship of ε(σ). A neural model of material (NMM) is a feed-forward layered neural network (FLNN) whose parameters were determined using the penalized least squares (PLS) method. A FLNN performing the inverse problem: σ(ε), using pseudo empirical patterns, was developed. Two models of NMM were developed, i.e. a standard model (SNN) and a model based on Bayesian inference (BNN). The properties of the models were compared on the example of a reference truss structure. The computations were performed by means of the hybrid FEM/NMM program, in which NMM developed previously described the current model of the material, and made it possible to explicitly build a tangent operator Et = dσ/dε. The neural model of material was applied to the analysis of the shakedown of load carrying capacity of an aluminum truss.

2

A semi-analytical method for identification of thin elastic plate parameters basing on LWM

Pabisek E., Waszczyszyn Z., Ambroziński Ł.

Computer Assisted Methods in Engineering and Science

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2014

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Vol. 21, no. 1

5--14

EN

A new semi-analytical method, discussed in the presented paper, is composed of two stages. Stage A corresponds to the direct analysis, in which the Lamb Waves Measurements (LWM) technique enables obtaining an experimental set of points D(fj , kj) Jj =1, where f and k are frequency and wavenumber, respectively. After the preprocessing in the transform space an experimental approximate curve kexp(f | D) can be formulated. In Stage B the identification procedure is simulated as a sequence of direct analyses. The dimensionless Lamb Dispersion curves are computed by means of the dimensionless simulation curve ksim(f | par), where the vector of plate parameters par = {E,ν, d, ρ} is adopted, in which Young modulus E, Poisson ratio ν, plate thickness d and density ρ are used. The main idea of the proposed approach is similar to that in the classical method of error minimization. In our paper we propose to apply the zero error value of relative criterion Reky = 0, cf. formula (15). The formula can be applied for the identification of a single plate parameter, assuming a fixed value of the other plate parameters. This approach was used in a case study, in which Stages A and B were analysed for an aluminum plate.

3

Analiza stanu naprężeń i przemieszczeń konstrukcji aluminiowej z wymienianymi elementami

Potrzeszcz-Sut B, Pabisek E.

Budownictwo i Architektura

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2013

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Vol. 12, nr 1

275--282

PL

Praca dotyczy nieliniowej analizy numerycznej naprężeń i przemieszczeń węzłów kratownicowej wieży aluminiowej. Założono model materiału Ramberga – Osgooda (RO) przedstawiający potęgową zależność między odkształceniem i naprężeniem: ε(σ). W celu identyfikacji zależności odwrotnej – σ(ε), dla materiału aluminiowego, zastosowano sztuczną sieć neuronową (SSN). W związku z koniecznością wzmocnienia konstrukcji, do układu wprowadzono sprężyste elementy stalowe. Przeprowadzono analizę stanu naprężeń i ekstremalnych przemieszczeń podczas cyklicznego obciążania i odciążania układu. Wykonano dwa rodzaje globalnych odciążeń – sprężyste i sprężysto – plastyczne. Przedstawione zostały zależności między wartością parametru obciążenia konfiguracyjnego, a wychyleniem wierzchołka A wieży. Analiza została wykonana za pomocą programu hybrydowego integrującego MES i SSN.

EN

The paper concerns the non-linear analysis of stresses and displacements in an aluminium truss tower. The Ramberg – Osgood material model was assumed. This model introduced power type relation between stresses and strains. In order to identify the inverse relation, a neural network was used. Because of the need to strengthen the tower, a number of aluminium bars was replaced by steel bars. The perfect elastic material model was assumed for the steel bars. The analysis of stresses and extreme displacements was performed during the cyclic loading and unloading of the system. Two global unloading processes were considered: elastic and elastic-plastic processes. The relationship between the load factor and deflection of the top of the tower is shown. Analysis was performed using a hybrid FEM/ANN program.

4

Identification of an equivalent model for granular soils by FEM/NMM/p-EMP hybrid system

Pabisek E.

Computer Assisted Mechanics and Engineering Sciences

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2011

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Vol. 18, no. 4

283-290

EN

The application of FEM/NMM/p-EMP computational hybrid system in formulation of the Neural Material Model (NMM) for granular soils is presented. NMM is a Multi Layer Preceptron formulated ’on-line’. The cumulative algorithm of the autoprogressive method was implemented into the FEM program. The patterns for NMM training were generated in the rigid strip footing analysis. Pseudo-empirical equilibrium paths p-EMP for veri?cation of the NMM were computed by a FEM program for the elastic-plastic Drucker-Prager material model. The discussed inverse problem of NMM identi?cation is illustrated by two study cases of footing: 1) rigid strip footing on plane semispace, 2) inclined slope analysis. It was numerically proved that the NMM identi?ed in the ?rst study case can be successfully applied to the analysis of the latter one.

5

Hybrid computational systems instructural mechanics

Waszczyszyn Z., Pabisek E., Kaliszuk J.

Czasopismo Techniczne. Mechanika

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2010

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R. 107, z. 4-M

135-146

EN

The first problem discussed in the paper is related to the reliability of structures. The simulation of the ultimate load of a steel girder is analized by means of a hybrid computational system FEM & ANN & p-EMP. The system consists of three components, with a low fusion grade. FEM is applied for 'off line' computing of the patterns for ANN training and testing. The trained ANN is then used for very fast generation of MC trials for the hybrid Monte Carlo method (HMC). The second problem corresponds to the identification of a neural material model (NMM) in elasto-plastic plane stress problems. The autoprogressive method (APM) was applied in a formulated hybrid system FEM/NMM/p-EMP with a very high fusion grade of components. The 'on line' interaction of all the components is applied at each load incremental step. In the third part of the paper the standing seminar on the application of ANN s in civil engineering, inspired by the ideas of the famous Professor Życzkowski's Seminar on applied mechanics, is briefly described.

PL

Pierwszy problem, analizowany w tym artykule, dotyczy analizy niezawodności konstrukcji. Nośność graniczna dźwigara stalowego jest symulowana za pomocą hybrydowego systemu obliczeniowego FEM & p-EMP. FEM jest stosowana do obliczania wzorców uczących i testujących ANN. Nauczona sieć służy do szybkiego generowania pseudolosowych próbek w symulacjach hybrydowej metody Monte Carlo (HMC). Drugi problem odnosi się do identyfikacji neuronowego modelu materiału ekwiwalentnego (NMM) w wybranych problemach płaskiego stanu naprężeń. Zastosowano system hybrydowy FEM/NMM/p-EMP charakteryzujący się bardzo wysokim stopniem integracji użytych komponentów. Do identyfikacji NMM zastosowano metodę autoprogresywną (AMP), która opiera się na interakcji 'on line' wszystkich komponentów na każdym przyroście obciążenia. Trzecia część pracy jest poświecona stałemu seminarium nt. stosowania ANNs w inżynierii lądowej, inspirowanego przez słynne Seminarium Profesora Życzkowskiego z zakresu mechaniki stosowanej.

6

Self-learning FEM/NMM approach to identification of equivalent material models for plane stress problem

Pabisek E.

Computer Assisted Mechanics and Engineering Sciences

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2008

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Vol. 15, No. 1

67-78

EN

The autoprogressive and cumulative algorithms, basing on `on line' formulation of patterns and the training of NMM (Neural Material Model), are evaluated to be comparable in case of uniaxial stress state problems. It is shown in the paper that for the plane stress boundary value problems the autoprogressive algorithm, in which NMM is trained for each load increment, is superior to the cumulative algorithm. In order to formulate a small NMM and accelerate the convergence of the iteration of computed equilibrium paths to the monitored paths, a smaller number of inputs NMM is discussed and a modified selection of the training patterns is applied. A new approach is proposed with respect to the designing of NMMs, combining the `on line' and `off line' training of neural networks. The discussed problems are illustrated with two study cases. They are related to the formulation of NMMs for the identification of equivalent materials in plane trusses made of the Ramberg–Osgood material and for elasto-plastic plane stress boundary value problems.

7

On algorithms for identification of a neural network based model of equivalent material in real structures

Pabisek E.

Archives of Civil Engineering

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2008

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Vol. 54, nr 2

395-404

EN

Neural network based material model (NMM) is discussed. NMM is formulated as an implicit model for an equivalent material of a structure, basing on displacements measured at selected points of the investigated structure. Two methods of training patterns generation were used. The "on line" autoprogressive Algorithm A and "batch mode" cumulative Algorithm B were discussed. These algorithms were modified and implemented for the pattern "on line" generation and NMM training. A plane truss, taken from, was analyzed using the incremental FE approach on the base of two stage procedure at each load incremental level, which ensures an appropriate response of the structure made of equivalent material on the base of monitored displacements. The iterative algorithms A and B enable formulation of a simple NMM which gives material identification with a great accuracy.

PL

Przedstawiono budowę i zastosowanie neuronowego modelu materiału (NMM). NMM jest sformuowany dla materiału ekwiwalentnego konstrukcji korzystając z przemieszczeń mierzonych w wybranych punktach analizowanej konstrukcji. Identyfikację NMM realizowano za pomocą dwóch algorytmów: autoprogresywnego Algorytmu A oraz kumulacyjnego Algorytmu B. Obydwa algorytmy zostały zmodyfikowane a następnie zastosowane do generowania wzorców służących do zaprojektowania i nauczenia sieci neuronowej czyli utworzenia neuronowego modelu materiału. Do analizy numerycznej wykorzystano wzorcową płaską kratownicę. NMM był formułowany w przyrostowym programie MES, podczas realizacji dwuetapowej procedury wykonywanej w czasie obliczeń dla każdego przyrostu obciążenia. Iteracyjne algorytmy A i B umożliwiają utworzenie prostych NMM, które pozwalają na identyfikację materiału z dużą dokładnością.

8

Neural analysis of elastoplastic plane stress problem with unilateral constraints

Pabisek E.

Computer Assisted Mechanics and Engineering Sciences

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2007

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Vol. 14, No. 3

497-507

EN

The paper is a development and continuation of paper [1] where the Panagiotopoulos approach was extended for the elastoplastic analysis. In case of elastic analysis the parameters of the Hopfield–Tank Neural Network (HTNN) are calibrated only once but the updating of the elastoplastic stiffness matrix needs an iteration of HTNN and FE system. The main problem is the matrix condensation repeated for each iteration step of the Newton–Raphson method. Besides all the improvements proposed in [2], a new interacting program has been implemented which enables a significant decrease of the processing time (number of iterations) in comparison with the time achieved in [1]. The results of the extensive numerical analysis are discussed for a tension perforated strip with a rigid bolt placed frictionlessly in a circular hole in the middle of the strip.

9

Elastoplastic analysis of plane steel frames by a new superelement

Waszczyszyn Z., Pabisek E.

Archives of Civil Engineering

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2002

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Vol. 48, nr 2

159-181

EN

In the paper a consistent, plastic-zone approach is discussed, associated with modeling on four levels, i.e. on the point, subelement, superelement and structural levels, respectively. The Return Mapping Algorithm is used on the point level. The reduced integration at two Gauss points and Simpson's quadrature formula are applied in the subelement. An iterative static condensation of subelements DOFs is explored in order to obtain the superelement matrices. A new superelement, composed of 12 irregular length subelements is examined also for the uniform load and for the 2nd order, geometrically nonlinear theory. Two calibrating frames are analyzed up to ultimate load considering either geometrically linear equations or the 2nd order theory. Single parameter proportional loading and unloading as well as a sequence of loadings are considered.

PL

Rozważa się konsystentne modelowanie w odniesieniu do czterech poziomów analizy, tj. poziomu punktu, podelementu, superelementu i całego układu. Algorytm RMA (Return Mapping Algorithm) jest stosowany na poziomie punktu. Zredukowane całkowanie w dwóch punktach Gaussa i kwadratura Simpsona stosuje się w podelemencie. Iteracyjna, statyczna kondensacja stopni swobody podelementów jest stosowana celem obliczenia macierzy superelementu. Nowy element, złożony z 12-tu podelementów o nieregularnej długości został przetestowany również dla obciążenia równomiernie rozłożonego i dla geometrycznie nieliniowej teorii rzędu II. Dwie ramy kalibrujące zostały obliczone aż do osiągnięcia nośności granicznej przyjmując teorię liniową lub teorię rzędu II. Jednoparametrowe, proporcjonalne obciążenie lub sekwencja obciążeń jednoparametrowych zostały przeanalizowane jak również zostały obliczone trwałe ugięcia ram.

10

Application of a Hopfield type neural network to the analysis of elastic problems with unilateral constraints

Waszczyszyn Z., Pabisek E.

Computer Assisted Mechanics and Engineering Sciences

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2000

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Vol. 7, No. 4

757-765

EN

On the base of Hopfield-Tank neural network the Panagiotopoulos approach is briefly discussed. The approach is associated with the analysis of quadratic programming problem with unilateral constraints. Then modifications of this approach are proposed. The original Panagiotopoulos approach is illustrated by the analysis of crack detachment in an elastic body. Efficiency of the proposed modifications is shown on a numerical example of an angular plate. Finally some special conclusions are expressed.

11

Hybrid NN/FEM analysis of the elastoplastic plane stress problem

Waszczyszyn Z., Pabisek E.

Computer Assisted Mechanics and Engineering Sciences

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1999

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Vol. 6, No. 2

177-188

EN

The back-propagation neural network was trained off line in order to simulate operation of the return mapping algorithm. Selection of patterns and the neural network training as well as testing processes are discussed in detail. The network was incorporated into the FE computer code ANKA as a neural procedure. The hybrid neural-network/finite-element-method program ANKA-H was used for the analysis of two elastoplastic plane stress examples: i) perforated tension strip, ii) notched beam. The results of computations point out quite good accuracy of the hybrid analysis. Some prospects of development of hybrid NN/FEM programs are given at the end of paper.