Elastic-plastic Structural Analysis Research Articles

Thermal Elastic–Plastic Analysis of Three-Dimensional Structures Using Face-Based Smoothed Point Interpolation Method

In this work, a face-based smoothed point interpolation method (FS-PIM) is formulated for three-dimensional (3D) thermal elastic-plastic analysis of structures. For this method, field functions are approximated using second order PIM shape functions and the face-based smoothing domains are used to perform the numerical integration. The material properties are considered to be temperature-dependent and the plastic behavior is studied through the Von Mises yield function. Numerical examples with different kinds of boundary conditions are investigated to verify the validity of the present method. The obtained results indicate that FS-PIM is an effective technique for the thermal elastic-plastic analysis of structures.

Failure of Hexagonal and Triangular Honeycomb Core Sandwich Panels

Honeycomb sandwich panels are used in aerospace structures for their high stiffness-to-mass ratio. Reducing structural mass is critical in aircraft and spacecraft development due to its direct impact on payload capacity and operational costs. Typically, hexagonal honeycombs manufactured by cold expansion of periodically bonded strips of metal or foils of other materials are used for sandwich construction. With rapid development in additive manufacturing, other core shapes with higher specific stiffness can now be considered as an alternative. The authors of this paper had previously evaluated triangular cores to have higher or comparable specific moduli as compared with other two-dimensional core shapes. Further, the panels constructed using triangular cores had higher stiffness than traditional hexagonal core panels. To consider practical use of the triangular cores, elastic-plastic structural analysis is performed to evaluate the strength and failure of sandwich panel construction. Load bearing capacity of triangular core panels under three-point bending, in-plane compressive loading, and transverse shear loading is evaluated using finite element software ABAQUS/Explicit. The comparison made between triangular core and hexagonal core sandwich panels having the same cell size and relative density showed that triangular cores outperform hexagonal cores for applications where in-plane loading is dominant, whereas, in terms of transverse shear and out-of-plane loading, triangular core panels tend to fail at lower loads and lower deflections.

Research on grind-hardening layer and residual stresses based on variable grinding forces

This paper analyzes the grinding force variation of grind-hardening process and proposes a simulation model to predict the residual stress profile based on the variable grinding forces. Time-dependent grinding force is discretized to calculate the heat flux intensity, which is applied on the actual contact length for the grinding temperature field, and the harden layer depth along the workpiece length is predicted. After that, the mechanical and thermal stress field is calculated with the results of variable grinding forces and grinding temperature, respectively. The loading stresses are coupled into an elastic-plastic structural analysis to estimate the residual stresses by defining indicator variables. Experimental results on the residual stress and the harden layer profile have validated the theoretical model.

Shakedown analysis of elastic-plastic structures considering the effect of temperature on yield strength: Theory, method and applications

According to the extended Melan's static theorem, theoretical and numerical aspects of the stress compensation method (SCM) are presented to perform shakedown analysis of elastic-plastic structures considering the effect of temperature on yield strength. Instead of constructing a mathematical programming formulation, this developed method consists of the two-level iterative scheme. The inner loop constructs the statically admissible self-equilibrating stress field, while the outer loop evaluates a sequence of decreasing load factors to approach to the shakedown limit multiplier. The yield strength considering temperature effect is updated based on the current temperature at each outer iteration, and the yield conditions are checked at all Gauss points. The numerical procedure is well incorporated into ABAQUS finite element code and used for calculating the shakedown limits of structures considering yield strengths as different functions of temperature under complex thermomechanical loading system. The method is validated by some plane stress and axisymmetric numerical examples with theoretical and numerical solutions, and subsequently applied to solve the practical shakedown problem of a pipe with oblique nozzle. The results demonstrate that the developed method is stable, accurate and efficient, and can effectively evaluate the shakedown limit of an elastic-plastic structure where the yield strength of material varies with temperature.

Dynamic Response Analysis of Elastic-plastic Structures with Component Mode Synthesis

This paper evaluates the validity of component mode synthesis (CMS) technique for dynamic response of elastic-plastic structures. A method incorporating elastic-plastic material behaviour and the fixed interface mode synthesis technology is presented. To do this, the incremental governing equations of elastic-plastic transient problem derived from nonlinear finite element theory are linearized in each time step, the tangent stiffness matrix is used to generate the basis vector of transformation matrix. Using the proposed method, the response of a simply supported beam loaded impulsively is examined. The Numerical results indicate that the proposed method is accurate, convergent and more efficient compared with the full order finite element model.

Artificial neural network-based response surface methods for reliability analysis of pre-stressed concrete bridges

Two artificial neural network (ANN)-based response surface methods for reliability analysis of pre-stressed concrete bridges are presented. The first method is the traditional ANN-based response surface method, originally introduced by Papadrakakis et al. in 1996 (Papadrakakis, M., Papadopoulos, V. and Lagaro, N., 1996. Structural reliability analysis of elastic-plastic structures using neural network and Monte carlo simulation. Computer Methods in Applied Mechanics and Engineering, 136, 145–163), which is applied here to the reliability analysis of pre-stressed concrete bridges. The second method is an improved ANN-based response surface method developed recently by the authors for the reliability analysis of truss structures, in which the key idea is that the uniform design method (UDM) is adopted to select training data for establishing an ANN model, thereby greatly improving the quality of training datasets for establishing an ANN model and dramatically reducing the required number of training datasets. There are two main objectives of the present work. Firstly, an attempt is made to extensively examine the performance of the traditional ANN-based response surface method since no detailed study has been carried out to investigate the effectiveness of this ANN-based response surface method on the basis of the reliability analysis of complicated structures such as pre-stressed concrete bridges. Secondly, the recently developed ANN-based response surface method is extended to the reliability analysis of pre-stressed concrete bridges. A detailed numerical investigation is carried out to compare the performance of the two methods.

Shakedown and collapse of elastic-plastic structures under variable and cyclic loads

The paper presents an introduction to the results obtained mainly by the author in shakedown analysis of elastic plastic structures, with the shakedown theorems for elastic plastic kinematic hardening materials playing the central role. Some illustrative examples of application are given.

An adaptive strategy for elastic-plastic analysis of structures with cracks

This work presents a methodology for self-adaptive finite element analysis of two-dimensional elastic-plastic structures. The self-adaptive process is based on an h-type refinement, with a posteriori error estimation. Two types of error estimators are available. The first is based on effective stress (Lee and Bathe, 1994) and the second is based on a ratio of plastic work (Peric et al., 1994). In the non-linear adaptive process for incremental plasticity analysis, a technique for interpolating analysis variables across distinct meshes (Lee and Bathe, 1994) is adopted. The von Mises yield criterion, with isotropic hardening, is adopted. Fracture problems are used to evaluate the performance of the adaptive process.

재생냉각형 가스발생기 챔버 구조해석

Elastic-plastic structural analysis for regenerative cooling chamber of gas generator was performed. Uniaxial tension test was conducted for STS316L at room and high temperature conditions to get the material data necessary for the structural analysis of the chamber which was operated under thermal load and high internal pressure. Physical properties including thermal conductivity, specific heat and thermal expansion were also measured. The structural analysis for four different types of regenerative cooling chamber of gas generator revealed that increased cooling performance decreased the thermal load and strain of the cooling channel structure. The results propose that in order for the regenerative cooling gas generator chamber to have high structural stability with endurance to high mechanical and thermal loads, it is important for the chamber to be designed to have high cooling performance.

액체로켓 연소기 재생냉각 챔버 구조설계

재생냉각형 액체로켓 연소기의 냉각채널 설계에 대한 탄-소성 구조설계를 수행하였다. 구조해석에 필요한 데이터를 얻기 위하여 여러 가지 온도에서 재생냉각 챔버 제작에 사용하는 구리합금의 단축인장시험을 수행하였다. 재료시험 결과 구리합금은 브레이징 공정 후에 연화되어 강도 값이 매우 저하되며 온도가 증가함에 따라 유동 응력 값이 더 작게 나타났다. 재료시험 데이터를 이용하여 냉각채널의 구조해석을 수행한 결과 채널 내부 냉각유체에 의한 내부압력보다 고온의 연소가스에 의한 열 하중에 의하여 채널의 변형이 심하게 발생함을 확인하였다. 따라서 기계적인 하중을 견딜 수 있는 한도 내에서 냉각채널의 두께를 감소시켜 열 하중을 최소화함으로서 연소기의 무게 감소, 냉각성능 향상, 그리고 구조적인 안정성을 향상시킬 수 있다는 것을 알 수 있었다. Elastic-plastic structural analysis for regenerative cooling chamber of liquid rocket thrust chamber is performed. Uniaxial tension test is also conducted for the copper alloy in order to get material data necessary for the structure analysis. The results of uniaxial tension test reveal that copper alloy become ductile after brazing process and flow stress becomes lower as temperature becomes higher. As a result of structural analysis using the material data, the deformation of cooling channel is more increased by thermal load than by internal pressure of cooling fluid. Therefore, the results of analysis show that structural stability and cooling performance of combustion thrust chamber which is designed to endure mechanical load and minimized a channel thickness are improved by decreased thermal load as possible.

Electromagnetic forming of aluminum alloy sheet: Free-form and cavity fill experiments and model

A series of high-rate electromagnetic-forming experiments are presented that consider free-forming and two configurations of cavity fill operations, one with a flat-bottomed die and the other with a hemispherical protrusion on the bottom of the die cavity. The experiments are performed on 1 and 1.6 mm AA5754 and 1 mm AA5182 aluminum alloy sheet; all of which are candidates for lightweight automotive structural applications. Increasing energy levels of discharge resulted in increased cavity fill and strain level in the formed parts. The effect of die geometry on formability, strain state and location of failure is examined. Numerical simulations of the high-rate deformation and structural impact that occur during electromagnetic forming are presented, and provide insight into the physics of the problem and the transient nature of this high-rate deformation process. A transient electromagnetic finite-element code is used to model the time-varying currents that are discharged through the coil in order to obtain the transient magnetic forces that are imparted to the workpiece. The body forces generated by electromagnetic induction are then used as the loading condition to model the high-rate deformation of the workpiece using an explicit dynamic finite-element code. A “two-way, loose coupling” of the electromagnetic analysis with the elastic-plastic structural analysis is utilized to account for the effect of changing workpiece geometry on the transient body forces. Validation of the numerical model is performed through comparison between predicted and measured strain distributions within the formed parts.

Electromagnetic forming of aluminium alloy sheet

A numerical method for modeling the high rate deformation and impact that occurs during the electromagnetic forming process is presented with supporting experimental data, used to validate the predictions. The numerical model employs loose two-way coupling of the electromagnetic analysis with the elastic-plastic structural analysis. An electromagnetic finite element code is used to model the time varying currents that are discharged through the coil in order to obtain the transient magnetic forces that are imparted to the workpiece. The body forces generated by electromagnetic induction are then used as the loading condition to model the high rate deformation of the workpiece using an explicit dynamic finite element code. A series of high rate electromagnetic forming experiments are performed on 1 and 1.6 mm AA5754 and 1 mm AA5182 aluminum alloy sheet. T he experiments consider free forming, while also serving as a basis to validate the predictive capability of the numerical models. The experiments exhibited high rate formability limits that were similar to conventional quasi-static forming limits. The numerical model accurately predicted the final geometry of the samples as well as the measured strain distributions.

PROFESSOR ALGIRDAS ČIŽAS AS FAMOUS SCIENTIST AND EDUCATOR/PROFESORIUS ALGIRDAS ČIŽAS - ŽYMUS MOKSLININKAS IR PEDAGOGAS

Algirdas Eduardas ČIžas is Professor of the Department of Strength of Materials, Director of the Lithuanian Centre for Quality Assessment in Higher Education. Prof A. Čižas was born on September 16, 1929 in a picturesque Lithuanian locality, Anykščiai. In 1952 he graduated from Kaunas Polytechnic Institute (Faculty of Civil Engineering). In 1953–57 editor and head of the Division of Technical Literature in a publishing house in Vilnius, in 1959–64 editor of Lithuanian encyclopedias. In 1967 a Doctoral student, then teacher, Associated Professor, since 1977 full Professor at the Vilnius Civil Engineering Institute (later Vilnius Technical University). In 1980–87 Dean of Civil Engineering Faculty, since 1995 Director of the Centre for Quality. More than 100 scientific publications on higher education problems and structural mechanics, optimisation methods. A. Čižas has introduced restrictions of stiffness, influence of a cross-sectional shape and a strain-hardening factor into optimisation theory of structural mechanics. The first paper “Application of mathematical programming methods for analysis of elastic-plastic structures with restricted deformation” (in Russian) was published in “Statybine mechanika” (Structural mechanics) issued by the Kaunas Polytechnic Institute in 1966. A. Čižas reported his research results at international conferences in Russia, Poland, Italy, United Kingdom, USA, etc. More than 25 years of publishing “Lithuanian Proceedings in Mechanics” (“Lietuvos mechanikos rinkinys)” (1968–94) are related to the development of Lithuanian research in mechanics. During the whole period A. Čižas was a managing editor of the journal. All the papers in volumes 1–32 of the LPM were published in Russian with Lithuanian and English summaries. After integration of the journals, results of research on mechanics are published in “Mechanika” (Mechanics) and “Statyba” (Civil Engineering). A. Čižas is a member of editorial boards of both journals, an author of the textbook “Strength of Materials. Mechanics of Structural Members” (1993, in Lithuanian), a co-author of the textbook “Problems on Strength of Materials with Comments” (1985). He has translated (from Russian into Lithuanian) more than ten books. Prof A. Čižas is a coordinator of drafting several legislative acts for higher education. Member of the Seimas of Sqjūdis (1988–90), member of the Lithuanian State Language Committee at the Seimas of the Republic of Lithuania, expert of Science Council of Lithuania.

Effects of Hypoelastic Model and Plastic Hardening on Numerical Simulation : Shear Deformation of 2-Dimensional Plane Block

In the present paper we give a finite-element formulation for large-deformation elastic-plastic structural analysis in order to study the effects of the utilized constitutive equation on numerical simulation. The general framework of the constitutive equation for large strain and rotation problems is based on hypoelasticity, where either Jaumann or Green stress rate is assumed. For the plastic hardening rule, the internal time theory is employed, which can be regarded as a combined nonlinear isotropic/kinematic hardening plasticity model retaining the concepts of 'yield surface' and 'normality rule'. Numerical examples of plane blocks subjected to shear deformation show how the fundamental features of mechanical response are affected by the constitutive equation employed.

Effects of Hypoelastic Model and Plastic Hardening on Numerical Simulation. Shear Deformation of 2-Dimensional Plane Block.

The present paper gives a finite-element formulation for largely deformed elastic-plastic structural analysis in order to study the effects of the constitutive equation utilized on numerical simulations. The general framework of the constitutive equation for large strain and rotation problems is based on hypoelasticity, where either Jaumann or Green stress-rate is assumed. As for the plastic hardening rule, the internal time theory is employed, which can be regarded as a combined nonlinear isotropic/kinematic hardening plasticity model retaining the concepts of 'yield surface' and 'normality rule.' Numerical examples of plane block subjected to shear deformation show the fundamental features of mechanical response affected by the employed consititutive equation.

Plastic node method considering strain-hardening effects

Extending the basic theory of the plastic node method (PNM), a general theory for the elasticplastic analysis of structures considering strain-hardening effects is proposed. In the plastic node method, plastic deformations of a finite element are concentrated at the nodes, while the inside of the element remains elastic. A strain-hardening rate for the plastic nodal displacement is proposed by equating the plastic work done at the plastic node with that evaluated in the actual elastic-plastic stress distribution within the element. For framed structures, this nodal-point strain-hardening rate gives a reasonable definition of strain-hardening rate at a plastic hinge subjected to combined loads. Two yield criteria for beam-column and shell elements are employed, one of which is based on a full plastic condition, while in the second criterion an intermediate plastic state between the initial yielding and the full yielding of sections is taken into account. Applying the extended theory of plastic node method, several examples including an elastic-plastic large deflection analysis of plates are shown, and the validity and usefulness of the proposed method are demonstrated.

Generation of dominant modes and reliability analysis of frames

The paper presents a technique for reliability analysis of frames using the stiffness matrix method of linear elastic and piecewise linear elastic-plastic structural analysis and the first order second moment reliability method. It involves automatic generation of stochastically dominant mechanisms (modes) and their safety margin equations and calculation of bounds on the system reliability. Based on the computational experiments, logical strategies are proposed for selection of plastic hinges and branching of failure paths to identify stochastically dominant mechanisms. The proposed method is illustrated with numerical examples. The results show very good agreement with the results of other research workers. The proposed method of generating stochastically dominant modes is simple and fairly efficient and less computer-time consuming.

Mathematical model for the analysis of elastic-plastic structures under repeated—variable loading

Mathematical model for the analysis of elastic-plastic structures under repeated—variable loading

Consideration and strategies in developing finite element software for desktop computers

During the revolution in the field of engineering which is based on the use of computers and numerical methods of calculation, an evolution has emerged. This concerns the development of desktop computers and finite element software suited for the small and cheap machines. By that it became possible to utilize this highly effective tool with only low investments necessary. Described are the way to and the characteristics of such a software package, consisting of a preprocessor, a temperature field analysis part, a linear‐elastic rigidity calculation part, a non‐linear elastic—plastic structural analysis part and a postprocessor.

Generalized Inverses in Elastic-Plastic Analysis of Structures∗

Abstract This paper deals with elastic-plastic analysis of skeletal structures that are subjected to proportionally increasing loading. It is assumed that no local unloading occurs (holonomic behavior) and that yield conditions are piecewise linearized. A quadratic programming problem, which arises from the application of the minimum complementary energy principle for such structures, is shown to have an explicit form of solution. The matrix expression of this solution involves certain modifications of the Bott-Duffin generalized inverse. This inverse can be effectively calculated for a given structure and allows one to obtain a unique stress distribution under agiven load. Moreover, if the load is prescribed up to an unknown scalar factor, the ultimate value of this multiplier (collapse load) and the elastoplastic stress state at collapse can be found by the same method