Multi-parameter Loading Research Articles

Развитие практического метода расчета элементов стальных конструкций на прочность

A method is proposed for studying the strength of elements of steel structures under multi-parameter loading, taking into account the mutual influence of forces according to the actual limit state corresponding to the criterion of maximum plastic deformation . The solution of the problem is carried out in dimensionless parameters in the reverse sequence, which reduces the calculation time by several orders of magnitude. Based on the analysis of the results obtained, there has been developed a practical method for calculating I-beam elements for strength, the reliability of which is confirmed by fairly good overlap with the data of the study. Thus, very significant strength reserves are revealed, namely, at two-parameter loads M <sub> x </sub>, M <sub> y </sub> (oblique bending) - 8...32 %; and N , M <sub> y </sub> (compression with bending from the wall plane) - 6…29 %; at three-parameter loading N , M <sub> x </sub>, M <sub> y </sub> for I-beams with the belt and wall area ratio widely used in design practice at - 10…45 %. The discovered strength reserves turned out to be very significant, which indicates the need to study elements with other types of cross sections.

Reserves of the bearing capacity of metal columns as part of a single-span frame with crane loads

The search for reserves of bearing capacity and improvement of the calculation of compressed-flexural metal columns is an urgent task. This makes it possible to more fully take into account the actual operation of structures and metal savings. An analysis of these and other issues is given in this paper on the basis of theoretical and experimental studies of life-size compressed-curved columns as part of a single-story and single-span industrial building with overhead cranes. The purpose of this work was to search for reserves of the bearing capacity of compressed-bent columns as part of the diameter of one-story single-span buildings with overhead cranes. As a result of the theoretical studies carried out, a method for calculating the stability of compression-bending columns as part of a cross section with crane loads has been developed. The technique takes into account the compatibility of the work of unevenly loaded columns in the frame and the shape of the deformation of the columns under the action of an active load. The estimated length calculated for frames with crane loads according to the proposed method is less than the estimated lengths according to current standards by 8-20%. To implement the tasks set in the experiment, a stand was developed and manufactured that allows testing the column as part of the frame and applying all types of vertical and horizontal loads to it. Experimental studies of full-scale compression-bending columns as part of a frame with the application of all loads that act on them (permanent, wind and crane) at different stages of the load, up to the exhaustion of the bearing capacity, made it possible to investigate the actual stress-strain state of the columns and their movement, bending of column base plates, development of current deformations in web flanges, local buckling of flanges and webs, general buckling of columns in the frame. For reconstructed industrial enterprises, a method for determining the reserves of bearing capacity for vertical load based on multiparameter loading of the diameter is proposed.

Upgrading of the recording system of complex loading testing machine

The effectiveness of experimental studies of the mechanical properties of materials and the reliability of the results obtained are determined by the technical level of testing machines. The stress-strain state of the object is monitored using recording sensors. The reading accuracy for the existing CL unit is 8%. However, this accuracy appeared insufficient when studying the developed plastic deformations. The problem of insufficient accuracy is partially related to the outdated recording system of the experimental setup, both when taking the results of the experiments and when managing the experiment. Getting of the reliable data upon complex loading is necessary to identify the reserves of the bearing capacity of structural elements in conditions of multi-parameter loading. All the experiments on a CL testing machine were carried out at room temperature. An additional amplifier of the electric signal of the strain gauge sensor was introduced to improve the accuracy of the readings of the recording system. The results of modernizing the recording system of the CL testing machine intended for static isothermal tests of tubular specimens are presented. The testing machine provides testing of the samples under axial tensile force and torque.

Расчет на прочность усиливаемых под нагрузкой стержневых элементов стальных конструкций при многопараметрическом нагружении

The article considers the methodology for structural analysis of reinforced under load open-section steel structure elements for strength with multi-parameter loading. In order to reduce the volume of calculations, the reverse course of solving the strength problem is proposed using the «Section» algorithm in dimensionless parameters. According to the limit state of the rod in the most loaded main section and given relative eccentricities, real acting forces are determined taking into account the elastic-plastic performance of the section.

A change in the deformation mechanism with a monotonous change of the load parameter

This work analyses the deformation of high-loaded structures for problems of strength and safety. Determining the load safety factor typically requires a series of calculations with successively increasing loads, up to fracture. In cyclic loading, each calculation is a numerical modeling of the structure behavior during several (or several tens) cycles up to stabilization to estimate the damage accumulated during one stable cycle. In multi-parameter loading, different load combinations may cause different mechanisms of structural deformation (i.e., different distributions of plastic strains and their velocities in the structure) with different consequences for the structure, thereby requiring different safety factors. At one-parameter loading, the assumption that the deformation mechanism remains the same for different load levels could reduce the required number of calculations. This article presents examples proving that this assumption could lead to incorrect results and requires careful verification.

Equivalent Uniaxial Cyclic Tensile Stress as an Energy Characteristic of Metal Fatigue under Multiparameter Loading

A concept of the equivalent stress as an energy characteristic of the material ability to resist deformation and fatigue cracking is introduced based on the principles of physical mesomechanics and synergetics. It is shown that the tensile curve of the material, the fatigue life diagram, and the kinetic curve for fatigue crack growth obtained under common experimental conditions can be considered as unified or "master" diagrams for material behavior description under multiparameter loading. Examples of determining the equivalent stress value and correction functions on the basis of the introduced concept are given for fatigue specimens subjected to biaxial cyclic loading and for in-service fatigue specimens of aircraft structures.

Strength of Plate with the Filled Crack under Multiparameter Loading

The problem of stressed state of an elastic plate weakened by narrow rectilinear through crack (slit) filled with low-modulus material is considered within framework the classical two-dimensional plate theory. For the inclusion of small width the hypothesis of elastic Winkler’s layer is accepted. The boundary problem for the pair of biharmonic equations with complicated boundary conditions on the cut is formulated. The analytical solution of singular integrodifferential equations of the problem is built for a case of elliptical form of slit and uniform multiparameter load (combined tension, shear, bending and twisting). The jumps of the displacements and the normal rotation angles on the cut, the stress intensity factors for crack tips and the stresses in the filler are obtained. Special attention is paid to the issue of limited equilibrium of composition. The two mechanisms of fracture are considered: cracking of the plate near the peak of a slit and breach of filler integrity. The first of them is described by the criterion of the linear mechanics of fracture and the second one is described by the classical theory of strength. The considered model of the filled slit allows analytically evaluating the results of the renovation of defective lamellar structures. The diagrams of limiting equilibrium of plate with filled slit are built for several options of two-parametric loading. The key parameters that determine the success of injection technology for repair of the cracked plate for a given loading trajectory are the relative stiffness and relative strength of the filler.

Optimal fatigue analysis of structures during complex loadings

A new framework for high cycle fatigue analysis of metallic structures under complex multi-parameter loadings was here developed. This allows to reduce the analysis on a 2-D window with a characterized one-parameter cyclic loading thanks to an equivalence rule relative to damage between any two loadings. The simplified inelastic analysis introduced by J. Zarka [J. Zarka et al. 1990. A new approach in inelastic analysis of structures. CADLM] was used to find the limit state of the structure. A new design rules for fatigue analysis by utilizing automatic learning systems was successfully performed. A database was built by coupling numerical simulations and experimental results on several welded specimens which are considered as a general structure in the proposed approach. This could be possible by the introduction of an intelligent description of a general fatigue case based on the actual theories and models. A software, FATPRO [M.I. Systems, FatPro, available at http://www.mzintsys.com/our_products_fatpro.html], based on this work has been developed at MZ Intelligent Systems.

Stability boundaries of two-parameter non-linear elastic structures

The load-bearing capacity of structures can be influenced by variations in parameters, such as initial geometric defects, multi-parameter loadings, material specifications and temperature. This paper aims to introduce a new formulation to trace the stability boundaries of two-parameter elastic structures. The proposed procedure can find a set of critical points, both limit and bifurcation ones, via a modified Newton’s method. In the authors’ formulation, the residual force is set to zero, and a critically constraint is satisfied simultaneously. Numerical examples presented in this paper demonstrate the efficiency of the suggested method.

Direct calculation of critical points in parameter sensitive systems

At critical points along the equilibrium path, sudden and sometimes catastrophic changes in the structural behaviour are observed. The equilibrium path, load-bearing capacity and locations of critical points can be sensitive to variations in parameters, such as geometrical imperfections, multi-parameter loadings, temperature and material properties. This paper introduces an incremental-iterative procedure to directly calculate the critical load for parameterized elastic structures. A modified Newton’s method is proposed to simultaneously set the residual force and the minimum eigenvalue of the tangent stiffness matrix to zero by using an iterative algorithm. To demonstrate the performance of this method, numerical examples are presented.

A convenient approach for estimating time-dependent structural reliability in the load space

A procedure, formulated in the space of the load processes, is described for estimating the reliability of structures subject to multi-parameter time-varying loading. For most realistic reliability problems the load process space is of low order. As a result, the required multidimensional integration is significantly simplified. The proposed approach also has well defined steps. As a result, there is increased transparency and reduced problems of integration instability and non-convergence. Both loads and resistances are described in terms of random variable parameters and time dependent structural resistances can be considered. Numerical examples are given to illustrate the proposed method. Example applications are given for a fixed base rigid-plastic portal frame subjected to time dependent loads and resistances. Linear and non-linear limit state equations and Normal and non-Normal distribution of the random variables are considered and compared, in some cases, to the results evaluated using Monte Carlo simulation.

LAYOUT AND SHAPE OPTIMIZATION OF ELASTOPLASTIC DISKS WITH BOUNDS ON DEFORMATION AND DISPLACEMENT1*,2†

ABSTRACT A design method is presented for layout optimization of linearly elastic–perfectly plastic disks subjected to multiparameter loading. The method is based on the static theorem of shakedown analysis and on the concept of porous material, where the material distribution of the discretized structure is described by the densities of the finite elements that are considered design variables. In addition to shakedown, two further compliance constraints are applied: bounds for the complementary strain energy of the residual stresses, and for the residual displacements. By the proper choice of these bounds the plastic behavior of the disk can be controlled and in special cases the elastic and fully plastic optimal solutions can be determined. The formulation of this problem yields to nonlinear mathematical programing. The application is illustrated by numerical examples. The method can also be applied to trusses, frames, and plates. *Communicated by M. Botkin. †Presented at ICTAM2000, held in Chicago in September 2000.

Optimal plastic limit and shake-down design of bar structures with constraints on plastic deformation

Optimal plastic design methods of discretized bar structures are presented where the objective function is the volume of the structure and the permanent deformations are controlled by introducing a constraint on the complementary strain energy of the residual internal forces. Single- and multiparameter loadings are considered and in the latter case the constraint on shakedown is also included in the optimal design procedure. Alternative formulations of the problems, where the complementary strain energy of residual forces is minimized at a given volume of the structure, are also presented. The proposed design methods are nonlinear and their solutions lead to nonlinear mathematical programming. Iterative solution techniques can also be efficiently applied. This is illustrated by an example.

Collapse limit surface generation for multiparametric loading

A systematic computational scheme for the generation of the global collapse load surface of skeletal structures under multiparameter loading is developed. The algorithm is based on identifying the relevant collapse facets in load space through a hyperplane generation type technique involving solution of a series of linear programming problems. Several examples are given to illustrate its intuitive simplicity and accuracy.

Multiparametric Limit Analysis of Frames: Part I—Model

Plastic flexural collapse of framed structures due to the action of independently varying loads is considered by the formulation of a multi‐objective linear programming model. The approach is based on a lower‐bound theorem for multiparameter loading. The solution of the model makes it possible to determine the permissible variation of loading parameters, the enumeration of failure modes under different load combinations, the generation of the global‐limit hypersurface of frames and demarcation of regions corresponding to different failure modes on this hypersurface. Numerical algorithms for the solution and illustrative examples are given in a companion paper.

Stability and Vibrations of Geometrically Nonlinear Cylindrically Orthotropic Circular Plates

The stability analysis of axisymmetrical equilibrium states of geometrically nonlinear, orthotropic, circular plates that are deformed by multiparameter loading, including thermal influence, is presented. The dynamic method (method of small vibrations) is used to accomplish this purpose. The behavior of the plate in different cases is revealed. In particular, it is shown that two different types of snapping processes can occur. The values of frequencies of small eigenvibrations from various cases have been calculated. These investigations are realized by numerical and qualitative methods. Here only the numerical results are presented.

Evaluation of upper bounds to shakedown loads for shells

A method of bounding the shakedown domain for shells is proposed. Starting from W.T. Koiter's ‘inadaptation’ theorem and using the consequences following from the associated flow rule for piece-wise linear yield surfaces a procedure is developed to bound from above the shakedown loading programme for a shell. For multi-parameter loadings a time independent interaction surface bounding the shakedown domain from above is obtained whenever the elastic and the limit analysis solutions for the individual loads are known. An example of shakedown interaction curve for a two-parameter loading of a cylindrical shell is given.