A Distributed Plasticity Approach for Steel Frames Analysis Including Strain Hardening Effects

This paper focuses on the creation and numerical application of physically nonlinear plane steel frames analysis problems. The frames are analysed using finite elements with axial and bending deformations taken into account. Two nonlinear physical models are used and compared – linear hardening and ideal elastic-plastic. In the first model, distributions of plastic deformations along the elements and across the sections are taken into account. The proposed method allows for an exact determination of the stress-strain state of a rectangular section subjected to an arbitrary combination of bending moment and axial force. Development of plastic deformations in time and distribution along the length of elements are determined by dividing the structure (and loading) into the parts (increments) and determining the reduced modulus of elasticity for every part. The plastic hinge concept is used for the analysis based on the ideal elastic-plastic model. The created calculation algorithms have been fully implemented in a computer program. The numerical results of the two problems are presented in detail. Besides the stress-strain analysis, the described examples demonstrate how the accuracy of the results depends on the number of finite elements, on the number of load increments and on the physical material model. COMSOL finite element analysis software was used to compare the presented 1D FEM methodology to the 3D FEM mesh model analysis

Numerical investigation of the elastic-plastic linear hardening stress-strain state of the frame element cross-section

The aim of this paper is to present a solution algorithm for determining the frame element crosssection carrying capacity, defined by combined effect of bending moment and axial force. The distributions of stresses and strains inside a cross-section made of linearly hardening material are analysed. General nonlinear stress-strain dependencies are composed. All relations are formed for rectangular cross-section for all possible cases of combinations of axial force and bending moment. To this end, five different stress-strain states are investigated and four limit axial force values are defined in the present research. The nonlinear problem is solved in MATLAB mathematical software environment. Stress-strain states in the cross-sections are investigated in detail and graphically analysed for two numerical experiments

Optimization-Based Elastic-Plastic Analysis of Steel Frames by Volumetric Plasticity Concept

Structures composed of physical nonlinear finite elements under bending and compression or tension are considered in this paper. Material nonlinearity is considered as linearly hardened. In case of material hardening, plastic strains do not concentrate in one point but distribute in the certain volumes of finite element. Volumes of plastic strains zones in frame structure elements impact on elasticity modules of these elements sections by decreasing them. Technique of such elasticity modules decrease in finite elements sections is suggested. To realize such structure analysis, a treatment of strains in mathematical model is changed. Now strains are treated not as rotation angles and elongations of finite elements, but as longitudinal strains. Mathematical model including above mentioned modifications is presented. Solving algorithm based on a modified Newton-Raphson method is particularly explained and employed for numerical example

Formulations of the deformable foundation contact problems

Up to now in many works a construction on elastic foundation was modelled by the Winkler's hypothesis. In this paper the flexible plate-foundation system is investigated as an interaction of separate elastic bodies, which lie on the contact surface. Such a problem formulation allowed to make more exact the stress and strain distribution in the construction and the contact surface, to estimate the dead weight of the foundation. The presented numerical examples are realised using computer programme COSMOS/M. The obtained results show evidently the expediency of the new method application in practice. First Published Online: 30 Jul 201

Analysis of construction on elastic foundation with evaluation of all system dead weight/Konstrukcijų ant tampraus pagrindo skaičiavimas įvertinant visos sistemos savąjį svorį

Solution of constructions on an elastic foundation was formulated as the contact problem [1], [2]. With such a formulation the stress and strain state is investigated at the contact of construction and foundation. Therefore, we can not evaluate the influence of elastic foundation dead weight for stress and strain distribution in the soil. The aim of this article is to solve this pressing problem, which allows to define in more precise way the stress and strain state in the system, and to evaluate not only the dead weight of the construction, but also the dead weight of foundation. The system “construction-substructure-foundation” is investigated as an interaction of separate bodies. Such a formulation allows to go over from solving contact problems to the solution of qualitatively new problems in which the distribution of stresses and strains in foundation along the depth is evaluated. Mathematical models in this article are realised by computer programme COSMOS/M. The stress-strain state is determined by describing the system “wall-substructure-foundation” of elements with different physical-mechanical indices. First Published Online: 30 Jul 201

Optimization of Bridge Trusses Height and Bars Cross-Sections

The problems of optimal design of truss-type structures, aimed at determining the minimal volume (weight) of the structure, while optimizing the bar cross-sections and the truss height, are considered. The considered problem is treated as a nonlinear problem of discrete optimization. In addition to the internal forces of tension or compression, the elements of the truss can have the bending moments. The cross-sections of the bars are designed of the rolled steel profiles. The mathematical models of the problem are developed, taking into account stiffness and stability requirements to structures. Nonlinear discrete optimization problems, formulated in this paper, are solved by the iterative method using the mathematical programming environment MATLAB. The buckling ratios of the bars under compression are adjusted in each iteration. The requirements of cross-section assortment (discretion) are secured using the method of branch and bound