Nonlinear analysis of structures

The development of nonlinear analysis techniques within the framework of the finite-element method is reported. Although the emphasis is concerned with those nonlinearities associated with material behavior, a general treatment of geometric nonlinearity, alone or in combination with plasticity is included, and applications presented for a class of problems categorized as axisymmetric shells of revolution. The scope of the nonlinear analysis capabilities includes: (1) a membrane stress analysis, (2) bending and membrane stress analysis, (3) analysis of thick and thin axisymmetric bodies of revolution, (4) a general three dimensional analysis, and (5) analysis of laminated composites. Applications of the methods are made to a number of sample structures. Correlation with available analytic or experimental data range from good to excellent

User's manual for GAMNAS: Geometric and Material Nonlinear Analysis of Structures

GAMNAS (Geometric and Material Nonlinear Analysis of Structures) is a two dimensional finite-element stress analysis program. Options include linear, geometric nonlinear, material nonlinear, and combined geometric and material nonlinear analysis. The theory, organization, and use of GAMNAS are described. Required input data and results for several sample problems are included

Nonlinear Analysis of Structures: Wind Induced Vibrations

The proceedings at hand are the result of the International Master Course Module: "Nonlinear Analysis of Structures: Wind Induced Vibrations" held at the Faculty of Civil Engineering at Bauhaus-University Weimar, Germany in the summer semester 2019 (April - August). This material summarizes the results of the project work done throughout the semester, provides an overview of the topic, as well as impressions from the accompanying programme. Wind Engineering is a particular field of Civil Engineering that evaluates the resistance of structures caused by wind loads. Bridges, high-rise buildings, chimneys and telecommunication towers might be susceptible to wind vibrations due to their increased flexibility, therefore a special design is carried for this aspect. Advancement in technology and scientific studies permit us doing research at small scale for more accurate analyses. Therefore scaled models of real structures are built and tested for various construction scenarios. These models are placed in wind tunnels where experiments are conducted to determine parameters such as: critical wind speeds for bridge decks, static wind coefficients and forces for buildings or bridges. The objective of the course was to offer insight to the students into the assessment of long-span cable-supported bridges and high-rise buildings under wind excitation. The participating students worked in interdisciplinary teams to increase their knowledge in the understanding and influences on the behaviour of wind-sensitive structures

Development of computer program NAS3D using Vector processing for geometric nonlinear analysis of structures

An algorithm for vectorized computation of stiffness matrices of an 8 noded isoparametric hexahedron element for geometric nonlinear analysis was developed. This was used in conjunction with the earlier 2-D program GAMNAS to develop the new program NAS3D for geometric nonlinear analysis. A conventional, modified Newton-Raphson process is used for the nonlinear analysis. New schemes for the computation of stiffness and strain energy release rates is presented. The organization the program is explained and some results on four sample problems are given. The study of CPU times showed that savings by a factor of 11 to 13 were achieved when vectorized computation was used for the stiffness instead of the conventional scalar one. Finally, the scheme of inputting data is explained

PLANS; a finite element program for nonlinear analysis of structures. Volume 2: User's manual

The PLANS system, rather than being one comprehensive computer program, is a collection of finite element programs used for the nonlinear analysis of structures. This collection of programs evolved and is based on the organizational philosophy in which classes of analyses are treated individually based on the physical problem class to be analyzed. Each of the independent finite element computer programs of PLANS, with an associated element library, can be individually loaded and used to solve the problem class of interest. A number of programs have been developed for material nonlinear behavior alone and for combined geometric and material nonlinear behavior. The usage, capabilities, and element libraries of the current programs include: (1) plastic analysis of built-up structures where bending and membrane effects are significant, (2) three dimensional elastic-plastic analysis, (3) plastic analysis of bodies of revolution, and (4) material and geometric nonlinear analysis of built-up structures

Advances in engineering science, volume 2

Papers are presented dealing with structural dynamics; structural synthesis; and the nonlinear analysis of structures, structural members, and composite structures and materials. Applications of mathematics and computer science are included

Numerical combination for nonlinear analysis of structures coupled to layered soils

This paper presents an alternative coupling strategy between the Boundary Element Method (BEM) and the Finite Element Method (FEM) in order to create a computational code for the analysis of geometrical nonlinear 2D frames coupled to layered soils. The soil is modeled via BEM, considering multiple inclusions and internal load lines, through an alternative formulation to eliminate traction variables on subregions interfaces. A total Lagrangean formulation based on positions is adopted for the consideration of the geometric nonlinear behavior of frame structures with exact kinematics. The numerical coupling is performed by an algebraic strategy that extracts and condenses the equivalent soil's stiffness matrix and contact forces to be introduced into the frame structures hessian matrix and internal force vector, respectively. The formulation covers the analysis of shallow foundation structures and piles in any direction. Furthermore, the piles can pass through different layers. Numerical examples are shown in order to illustrate and confirm the accuracy and applicability of the proposed technique

A NEW ALGORITHM IN NONLINEAR ANALYSIS OF STRUCTURES USING PARTICLE SWARM OPTIMIZATION

Solving systems of nonlinear equations is a difficult problem in numerical computation. Probably the best known and most widely used algorithm to solve a system of nonlinear equations is Newton-Raphson method. A significant shortcoming of this method becomes apparent when attempting to solve problems with limit points. Once a fixed load is defined in the first step, there is no way to modify the load vector should a limit point occur within the increment. To overcome this defect, displacement control methods for passing limit points can be used. In displacement control method, the load ratio in the first step of an increment is defined so that a particular key displacement component will change only by a prescribed amount. In this paper the load ratio is obtained using particle swarm optimization (PSO) algorithm so that the complex behavior of structures can be followed, automatically. Design variable is load ratio and its unbalanced force is also considered as objective function in optimization process. Numerical results are performed under geometrical nonlinear analysis, elastic post-buckling analysis and inelastic post-buckling analysis. The efficiency and accuracy of proposed method are demonstrated by solving these examples. 

Nonlinear analysis of structures on elastic half-space by a FE-BIE approach

In the present dissertation, a numerical model able to study the non-linear behaviour of structures on elastic half-space is presented. The work takes into account for first the geometric non-linearity of beams and frames on elastic half-plane, namely in plane strain or plane stress condition. This problem is important in many engineering fields and it has been studied in the past by many researchers for the design of sandwich panels in aerospace industry. Recently, this problem has been studied in relation to the buckling of thin films on elastic supports for electronic design. The problem is solved by means of a mixed variational formulation, which assumes as independent fields the displacements of the structure and the contact pressures between foundation and halfspace. The relation between surface displacement and pressure is given by the Flamant solution, which furnishes the half-plane displacement generated by a concentrated force. The second order effects due to axial loads applied on the structure are added to the total potential energy of the system in order to perform buckling analyses. Then, the model is discretized by subdividing the structure into finite elements (FEs) and simplifying contact pressures by a piecewise constant function. Hence, the stationarity conditions of the total potential energy written in discrete form furnish a system of equations which can be solved easily. A soil-structure interaction (SSI) parameter taking into account both the slenderness of the foundation beam and the stiffness of the soil is introduced. The present model was introduced for the first time by Tullini and Tralli (2010) but it was limited to linear elastic analysis. In this case, the model is extended for studying the stability of beams on elastic half-plane, considering both Euler-Bernoulli and Timoshenko beam. In the first chapter, the present model for an Euler-Bernoulli beam on elastic half-plane is compared with a traditional model characterized by the half-space modelled by two-dimensional (2D) FEs. The present model turns out to be efficient and faster than the traditional model. Then, the stability of beams with finite length and with different end restraints is deeply discussed by determining critical loads and the corresponding mode shapes, varying the SSI parameter. Numerical examples are in good agreement with analytic solutions for the case of the beam with sliding ends. Critical loads converge to the values of a beam with infinite length on elastic half-plane and on a set of equidistant supports. The cases of beam with pinned and free ends furnish new estimates of critical loads, which are less than that for the beam with sliding ends and which are characterized by mode shapes with great deflections close to beam ends. In the second chapter, the stability of Timoshenko beams on elastic half-space is discussed. The present model is compared with a traditional model where both beam and half-plane are modelled by 2D FEs. For stiff or quite stiff beams on soft half-plane, the present model is fast and efficient, whereas for slender beams on stiff half-plane, the present model gives critical loads greater than the ones obtained with the traditional model. Differences are caused by the second order effects of the half-plane, which are taken into account in the traditional model. Then, in the third chapter, structures on half-plane are studied taking into account the material nonlinearity for the structure. A lumped plasticity model is considered and flexural plastic hinges are introduced into the discrete model of slender beams and frames on elastic half-plane. For simplicity, a rigid-perfectly plastic moment-rotation relationship is adopted for describing the behaviour of plastic hinges. Material nonlinearity is introduced into the discrete model following an efficient approach adopted for representing semi-rigid connections of frames. The approach gives the possibility to keep the same number of beam FEs and degrees of freedom of the original model, whereas potential plastic hinges are added to beam FE ends by simply modifying the corresponding stiffness matrices. Hence, incremental analyses of beams and frames are performed by placing potential plastic hinges close to concentrated loads and at beam-column connections. In the fourth chapter of the thesis, the discrete model of a beam on elastic half-plane is extended to the three-dimensional case for performing static and buckling analysis of foundation beams. Beams on 3D half-space are important in civil engineering field and they may adopted for representing shallow foundations on elastic soil. In this case, the relation between surface displacements and contact pressure is given by Boussinesq solution. The flexibility matrix of the soil is first determined for solving the Galerkin boundary element method, in order to study the indentation of the half-space by a rigid square punch and determining the displacements generated by uniform pressure distributions over rectangular areas. In both cases, the half-space surface is discretized in both plane directions adopting power graded meshes characterized by very small surface discretizations close to surface edges. Then, Euler-Bernoulli and Timoshenko beams on 3D halfspace subject to different loads are studied and displacements, surface pressures and bending moments are determined. Finally, the stability of Euler-Bernoulli beams on 3D half-space with finite length and different end restraints is considered. Critical loads and mode shapes are similar to those obtained for the 2D case in the fist chapter, however in this case, results are strictly dependent on the ratio between beam length and width

Investigating a hybrid perturbation-Galerkin technique using computer algebra

A two-step hybrid perturbation-Galerkin method is presented for the solution of a variety of differential equations type problems which involve a scalar parameter. The resulting (approximate) solution has the form of a sum where each term consists of the product of two functions. The first function is a function of the independent field variable(s) x, and the second is a function of the parameter lambda. In step one the functions of x are determined by forming a perturbation expansion in lambda. In step two the functions of lambda are determined through the use of the classical Bubnov-Gelerkin method. The resulting hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Bubnov-Galerkin methods applied separately, while combining some of the good features of each. In particular, the results can be useful well beyond the radius of convergence associated with the perturbation expansion. The hybrid method is applied with the aid of computer algebra to a simple two-point boundary value problem where the radius of convergence is finite and to a quantum eigenvalue problem where the radius of convergence is zero. For both problems the hybrid method apparently converges for an infinite range of the parameter lambda. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed