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Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

In this paper, the authors aim to propose an effective method to indirectly determine nonlinear elastic shear stress-strain constitutive relationships for nonlinear elasticity materials, and then study the nonlinear free torsional vibration of Al–1%Si shaft.

In this study the authors use BoxLucas1 model to fit the determined-experimentally nonlinear elastic normal stress–strain constitutive relationship curve of Al–1%Si, a typical case of isotropic nonlinear elasticity materials, and then derive its nonlinear shear stress-strain constitutive relationships based on the fitting constitutive relationships and general equations of plane-stress and plane-strain transformation. Hamilton’s principle is utilized to gain nonlinear governing equation and boundary conditions for free torsional vibration of Al–1%Si shaft. Differential quadrature method and an iterative algorithm are employed to numerically solve the gained equations of motion.

The effect of four variables, namely dimensionless fundamental vibration amplitude ϑmax, radius α and length β, and nonlinear-elasticity intensity factor δ, on frequencies and mode shapes of the shafts is obtained. Numerical results are in good agreement with reference solutions, and show that compared with linearly elastic shear stress-strain constitutive relationships of the shafts made of the nonlinear elasticity materials, its actual nonlinearly elastic shear stress-strain constitutive relationships have smaller torsion frequencies. In addition, but β having opposite hardening effect, the rest of the four variables have softening effect on nonlinearly elastic torsion frequencies. Eventually, taking into account nonlinearly elastic shear stress-strain constitutive relationships, changes of the four factors, i.e. ϑmax, α, β and δ, cause inflation and deflation behaviors of mode shapes in nonlinear free torsional vibration.

The study could provide a reference for indirectly determining nonlinear elastic shear stress-strain constitutive relationships for nonlinear elasticity materials and for structure design of torsional shaft made of nonlinear elasticity materials.

This paper aims to present a new numerical model for the stability and load‐bearing capacity computation of space reinforced‐concrete (R/C) frame structures. Both material and geometric nonlinearities are taken into account. The R/C cross‐sections are assumed to undergo limited distortion under torsional action.

A simple, global discretization using beam‐column finite elements is preferred to a full, global discretization using 3D elements. This is more acceptable from a practical point of view. The composite cross‐section is discretized using 2D elements to apply the fiber decomposition procedure to solve the material and geometrical nonlinear behavior of the cross‐section under biaxial moments and axial forces. A local discretization of each beam element based on the comparative body model (i.e. a prismatic body discretized using brick elements, element by element, during the incremental‐iterative procedure) allows determining the torsional constant of the cross‐section under limited warping. The classical global iterative‐incremental procedure is then used to solve the resulting material and geometric nonlinear problem.

It has been noticed that, in case of a limited distortion of the cross‐section, the torsional constant of homogeneous (linear elastic) materials is greater than the one obtained from the Saint‐Venant theory. However, due to low‐tensile strength of concrete materials, the torsional constant decreases significantly after an early loading phase, primarily due to the lack of reinforcing flanges.

The current study does not cover the torsion analysis of R/C cross‐section with stirrups. Besides, the bond‐slip effect between concrete and steel reinforcement is not taken into account, nor is the local buckling of the beam flanges and rebar.

This new numerical model has been implemented in a computer program for effectively computing the nonlinear stability and load bearing capacity of space R/C frames.

The authors believe that the comparative body model should bring a new approach to the solution of torsion problems with limited distortion of cross‐sections in material and geometric nonlinear analysis of space R/C frames.

The purpose of this study is to present a finite element (FE) implementation of phenomenological three-dimensional viscoelastic and viscoplastic constitutive models for long term behaviour prediction of polymers.

The method is based on the small strain assumption but is extended to large deformation for materials in which the stress-strain relation is nonlinear and the concept of incompressibility is governing. An empirical approach is used for determining material parameters in the constitutive equations, based on measured material properties. The modelling process uses a spring and dash-pot and a power-law approximation function method for viscoelastic and viscoplastic nonlinear behaviour, respectively. The model improvement for long term behaviour prediction is done by modifying the material parameters in such a way that they account for the current test time. The determination of material properties is based on the non-separable type of relations for nonlinear materials in which the material properties change with stress coupled with time.

The proposed viscoelastic and viscoplastic models are implemented in a user material algorithm of the FE general-purpose program ABAQUS and the validity of the models is assessed by comparisons with experimental observations from tests on high-density polyethylene samples in one-dimensional tensile loading. Comparisons show that the proposed constitutive model can satisfactorily represent the time-dependent mechanical behaviour of polymers even for long term predictions.

The study provides a new approach in long term investigation of material behaviour using FE analysis.

Scholars mainly propose and establish theoretical models of cumulative fatigue damage for their research fields. This review aims to select the applicable model from many fatigue damage models according to the actual situation. However, relatively few models can be generally accepted and widely used.

This review introduces the development of cumulative damage theory. Then, several typical models are selected from linear and nonlinear cumulative damage models to perform data analyses and obtain the fatigue life for the metal.

Considering the energy law and strength degradation, the nonlinear fatigue cumulative damage model can better reflect the fatigue damage under constant and multi-stage variable amplitude loading. In the following research, the complex uncertainty of the model in the fatigue damage process can be considered, as well as the combination of advanced machine learning techniques to reduce the prediction error.

This review compares the advantages and disadvantages of various mainstream cumulative damage research methods. It provides a reference for further research into the theories of cumulative fatigue damage.

In high voltage direct current cable systems, cable joints are known as the least reliable components due to the use of multiple dielectrics. Resulting from the electric field and temperature depending conductivity of the different dielectrics, field enhancement at critical areas, e.g. triple points, may result in accelerated aging and the failure of the component. To reduce the stress, different field grading techniques are applied. The purpose of this study is to investigate different grading techniques for cable joints. Different shapes of the electrode and a varying nonlinear conductivity of field grading materials (FGM) are used for the simulation of the electric field.

Coupled electro-thermal field simulations are applied for different joint geometries, to obtain the stationary electric field. Electric field simulations in cable joint using geometric and nonlinear field grading techniques are shown.

Using the geometric field grading, the shape of the stress cone determines the field values in critical areas (triple points). High stress reduction is obtained for a certain curvature of the stress cone. For the nonlinear stress control, materials with a higher conductivity in comparison to the cable and the joint material are used. A field reduction is obtained by increasing the total conductivity. On the other hand, this is also increasing the insulation losses within the total FGM. More applicable is the decrease of the switching field or the increase of nonlinearity, which is only locally increase the conductivity and the insulation losses. Furthermore, simulations results show that an approximately constant field reduction is obtained, if the nonlinearity is above a certain threshold.

This study is restricted to a field dependency of FGM only. For impulse voltages, high temperature and electric conductivity values my result in a thermal runaway. Furthermore, only direct current field grading techniques are studied.

The field grading of cable joints, using geometric and nonlinear techniques, is analyzed. A comparison between the electric field, by varying the curvature of the ground stress cone or the FGM conductivity constants in a complex joint geometry is novel. With its effect on the electric fields, general requirements for the geometry (geometric field grading) or the values of the FGM constants (nonlinear field grading) are defined to obtain a sufficient field grading.

Super304H steel is a new fine-grained austenitic heat-resistant stainless steel developed in recent years, and it is widely used in high temperature section superheater and reheater tubes of ultra-supercritical thermal power units’ boiler. Currently intergranular corrosion (IGC) has occurred in a few austenitic stainless steel tubes in ultra-supercritical units and led to boiler leakage. The purpose of this paper is to find a nondestructive method to quickly and easily detect IGC of austenitic stainless steel tube.

This paper uses the nonlinear characteristics of ultrasonic propagation in steel tube to detect the IGC of Super304H tube.

The experimental results show that the nonlinear coefficient generally increases sensitively with the degree of IGC; hence, the nonlinear coefficient can be used to assess IGC degree of tubes, and the nonlinear coefficient measurement method is repeatable for the same tube.

A theory of how IGC would affect the ultrasonic signals and lead to a nonlinear response needs further research.

A nondestructive method to quickly and easily detect IGC is provided.

Using ultrasonic nonlinear coefficient to assess IGC degree of tubes is a new try.

This paper provides a new way to test IGC.

Eddy currents are investigated in a ferromagnetic bar exposed to a transverse magnetic field. Such an open boundary field problem is analysed applying the Galerkin finite element method coupled with a separation of variables. A steady state is considered, introducing time periodic conditions. The resultant system of nonlinear equations is solved using an iterative procedure based on Brouwer's fixed‐point theorem referred to the nonlinear material reluctivity. Numerical results are presented for a massive conductor made of cast steel and cast iron. The eddy‐current distribution and characteristics of power losses are illustrated in a graphic form.

Digital materials are composed of many discrete voxels placed in a massively parallel layer deposition process, as opposed to continuous (analog) deposition techniques. The purpose of this paper is to explore the wide range of material properties attainable using a voxel‐based freeform fabrication process, and demonstrate in simulation the versatility of fabricating with multiple materials in this manner.

A representative interlocking voxel geometry was selected, and a nonlinear physics simulator was implemented to perform virtual tensile tests on blocks of assembled voxels of varying materials. Surface contact between tiles, plastic deformation of the individual voxels, and varying manufacturing precision were all modeled.

By varying the precision, geometry, and material of the individual voxels, continuous control over the density, elastic modulus, coefficient of thermal expansion, ductility, and failure mode of the material is obtained. Also, the effects of several hierarchical voxel “microstructures” are demonstrated, resulting in interesting properties such as negative Poisson's ratio.

This analysis is a case study of a specific voxel geometry, which is representative of 2.5D interlocking shapes but not necessarily all types of interlocking voxels.

The results imply that digital materials can exhibit widely varying and tunable properties in a single desktop fabrication process.

The paper explores the vast potential of tunable materials, especially using the concept of voxel microstructure, applicable primarily to 3D voxel printers but also to other multi‐material freeform fabrication processes.

The purpose of this paper is to implement the Anderson acceleration for different formulations of eletromagnetic nonlinear problems and analyze the method efficiency and strategies to obtain a fast convergence.

The paper is structured as follows: the general class of fixed point nonlinear problems is shown at first, highlighting the requirements for convergence. The acceleration method is then shown with the associated pseudo-code. Finally, the algorithm is tested on different formulations (finite element, finite element/boundary element) and material properties (nonlinear iron, hysteresis models for laminates). The results in terms of convergence and iterations required are compared to the non-accelerated case.

The Anderson acceleration provides accelerations up to 75 per cent in the test cases that have been analyzed. For the hysteresis test case, a restart technique is proven to be helpful in analogy to the restarted GMRES technique.

The acceleration that has been suggested in this paper is rarely adopted for the electromagnetic case (it is normally adopted in the electronic simulation case). The procedure is general and works with different magneto-quasi static formulations as shown in the paper. The obtained accelerations allow to reduce the number of iterations required up to 75 per cent in the benchmark cases. The method is also a good candidate in the hysteresis case, where normally the fixed point schemes are preferred to the Newton ones.