Topology optimization of structures under multiple load cases using a fiber-reinforced composite material model

This paper presents a method to optimize the topology of structures under multiple load cases with stress constraints. Fiber-reinforced orthotropic composite is employed as the material model to simulate the constitutive relation of truss-like continua. The fiber densities and orientations at the nodes are taken as design variables. First, for each load case, the fiber orientations are aligned with the orientations of principal stress and the fiber densities are adjusted according to the strains along the fiber orientations. Then, to optimize the structure, the fiber densities and orientations under multiple load cases are determined by constraining its elastic matrix to approach the elastic matrix of the optimum structures defined for each single load case. Finally the member distribution in the optimal structure is suggested by the continuous lines formed according to the fiber densities and orientations. Several examples are presented to demonstrate the effectiveness of the proposed approach.     

Stable numerical integration of dynamical systems subject to equality state-space constraints

Numerical simulation of constrained dynamical systems is known to exhibit stability problems even when the unconstrained system can be simulated in a stable manner. We show that not the constraints themselves, but the transformation of the continuous set of equations to a discrete set of equations is the true source of the stability problem. A new theory is presented that allows for stable numerical integration of constrained dynamical systems. The derived numerical methods are robust with respect to errors in the initial conditions and stable with respect to errors made during the integration process. As a consequence, perturbations in the initial conditions are allowed. The new theory is extended to the case of constrained mechanical systems. Some numerical results obtained when implementing the numerical method here developed are shown.     

Concrete columns confined by fiber composite wraps under combined axial and cyclic lateral loads

This paper presents nonlinear finite element analysis of fiber reinforced polymer (FRP) jacketed reinforced concrete columns under combined axial and cyclic lateral loadings. Large-scale control and FRP-wrapped reinforced concrete columns (762 mm in diameter and 4978 mm in height) were modeled using the nonlinear finite element analysis software MARC™. The models were capable of allowing for the degradation of the stiffness under cyclic loading. The finite element analysis results indicated that reinforced concrete columns externally wrapped with the FRP fabric in the potential plastic hinge location at the bottom of the column showed significant improvement in both strength and ductility capacities, and the FRP jacket could be used to delay the degradation of the stiffness of reinforced concrete columns.     

The buckling of FGM truncated conical shells subjected to combined axial tension and hydrostatic pressure

The purpose of this paper is to investigate the elastic buckling of FGM truncated thin conical shells under combined axial tension and hydrostatic pressure. Here axial tensions are separately applied to small and large bases of the truncated conical shell, respectively. It is assumed that the cone is a mixture of metal and ceramic, and that its properties changes as the power and exponential functions of the shell thickness. After giving the fundamental relations, the stability and compatibility equations of an FGM truncated conical shell, subject to combined axial tension and hydrostatic pressure, have been derived. Applying Galerkin’s method general formulas have been obtained for the critical combined and separate loads of FGM conical shells. The appropriate formulas for homogenous and FGM cylindrical shells are found as a special case. Effects of changing shell characteristics, material composition and volume fraction of constituent materials on the critical combined and separate loads of FGM shells with simply supported edges are also investigated. The results obtained for homogeneous cases are compared with their counterparts in the literature.     

Experimental investigations on buckling of cylindrical shells under axial compression and transverse shear

This paper presents experimental studies on buckling of cylindrical shell models under axial and transverse shear loads. Tests are carried out using an experimental facility specially designed, fabricated and installed, with provision forin-situ measurement of the initial geometric imperfections. The shell models are made by rolling and seam welding process and hence are expected to have imperfections more or less of a kind similar to that of real shell structures. The present work thus differs from most of the earlier investigations. The measured maximum imperfections δ_max are of the order of ±3t (t = thickness). The buckling loads obtained experimentally are compared with the numerical buckling values obtained through finite element method (FEM). In the case of axial buckling, the imperfect geometry is obtained in four ways and in the case of transverse shear buckling, the FE modelling of imperfect geometry is done in two ways. The initial geometric imperfections affect the load carrying capacity. The load reduction is considerable in the case of axial compression and is marginal in the case of transverse shear buckling. Comparisons between experimental buckling loads under axial compression, reveal that the extent of imperfection, rather than its maximum value, in a specimen influences the failure load. Buckling tests under transverse shear are conducted with and without axial constraints. While differences in experimental loads are seen to exist between the two conditions, the numerical values are almost equal. The buckling modes are different, and the experimentally observed and numerically predicted values are in complete disagreement.     

Study of gate loads related to stress states in mass-flow bins during bulk solids filling and settlement

This paper concerns the determination of the loads on discharge isolating gates of mass-flow bins such as those used in the coal and iron ore industries for train loading. The gate loads are closely associated with the stress states of the bulk solids that are difficult to determine since they are highly dependent on the degree of the compressibility of the bulk solids and the rigidity of the gate. The so-called j factor as outlined in the Australian Standard 3774-1996 is incorporated in the gate load analysis to account for these properties. In this study, an analytical review of gate loads is combined with an experimental study employing a pilot mass-flow bin handling iron ore and plastic pellets. Of particular interest are the transient load changes due to the time-dependent settling of the bulk solid. The research findings are presented along with guidelines to assist the bin gate design.     

Optimization of volume fractions for functionally graded panels considering stress and critical temperature

Volume fraction optimization of Functionally Graded Materials (FGMs) is investigated considering stress and critical temperature. Material properties are assumed to be temperature dependent, and are assumed to be varied continuously in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituent materials. The effective material properties are obtained by applying linear rule of mixtures. The 3-D finite element model is adopted using an 18-node solid element to analyze more accurately the variation of material properties and temperature field in the thickness direction. For the various FGMs volume fraction distributions, mechanical stress analysis and thermo-mechanical buckling analysis are performed to get the critical conditions. Finally, the optimal designs of FGMs panels are investigated for stress reduction and improving thermo-mechanical buckling behavior.     

Topology optimization for crashworthiness of thin-walled structures under axial crash considering nonlinear plastic buckling and locations of plastic hinges

Although topology optimization is established for linear static problems, more effort is required for solving nonlinear plastic problems. A new topology optimization approach with equivalent static loads (ESLs) is suggested to find the optimum topologies and locations of plastic hinges of thin-walled crash boxes by considering crash-induced deformation, the main crash energy-absorbing mechanism. Together with finite element method crashworthiness analyses, considering all nonlinearities with rate-dependent plasticity, the method was developed using an appropriate time-incremental scheme of ESLs without removing any high values of loads. Analyses show that the crash boxes with optimum topologies have energy-absorbing capabilities equivalent to the original structure. The proposed method is evaluated for two crashes: a crash box at low speed and a double cell subjected to high-speed collision. The results indicate that this method captures nonlinear crushing behaviours and accurate locations of plastic hinges where, if proper reinforcements are made, energy absorption can be enhanced.     

Numerical simulation of axially loaded concrete columns under transverse impact and vulnerability assessment

With a view to assessing the vulnerability of columns to low elevation vehicular impacts, a non-linear explicit numerical model has been developed and validated using existing experimental results. The numerical model accounts for the effects of strain rate and confinement of the reinforced concrete, which are fundamental to the successful prediction of the impact response. The sensitivity of the material model parameters used for the validation is also scrutinised and numerical tests are performed to examine their suitability to simulate the shear failure conditions. Conflicting views on the strain gradient effects are discussed and the validation process is extended to investigate the ability of the equations developed under concentric loading conditions to simulate flexural failure events. Experimental data on impact force–time histories, mid span and residual deflections and support reactions have been verified against corresponding numerical results. A universal technique which can be applied to determine the vulnerability of the impacted columns against collisions with new generation vehicles under the most common impact modes is proposed. Additionally, the observed failure characteristics of the impacted columns are explained using extended outcomes. Based on the overall results, an analytical method is suggested to quantify the vulnerability of the columns.     

Behavior of corrosion-damaged RC columns wrapped with FRP under combined flexural and axial loading

This paper presents the results of a research program aimed at investigating the effectiveness of carbon fiber-reinforced polymers (CFRP) to upgrade corrosion-damaged eccentrically loaded reinforced concrete (RC) columns. A total of 16 square RC columns with end corbels were constructed. Test specimen had an overall length of 1200 mm whereas each end corbel had a cross section of and a length of 350 mm. The specimen in the test region was having longitudinal steel ratio of 1.9%. The damaged specimens were exposed to 30 days of accelerated corrosion that corresponded to a steel mass loss of about 4.25%. The main test parameters were the CFRP repair scheme (no wrapping, full-wrapping, and partial-wrapping) and the eccentricity-to-section height (e/h) ratio (0.3, 0.43, 0.57, and 0.86). The strength of the damaged columns fully wrapped with CFRP was up to 40% higher than that of the control undamaged columns. The strength gain was inversely proportional to the eccentricity ratio. Partial CFRP-wrapping was 8% less effective than full CFRP-wrapping at nominal e/h of 0.3. At higher e/h values, the confinement level had a negligible effect on the columns’ strength. An analytical model was then proposed to predict the columns’ strength under eccentric loading. A comparative analysis between predicted and experimental results demonstrated the model’s accuracy and reliability.     

Fracture of austenitic steel subject to a wide range of stress triaxiality ratios and crack deformation modes

The stress triaxiality ratio (hydrostatic pressure divided by von Mises equivalent stress) strongly affects the fracture behaviour of materials. Various fracture criteria take this effect into consideration in their effort to predict failure. The dependency of the fracture locus on the stress triaxiality ratio has to be investigated in order to evaluate these criteria and improve the understanding of ductile fracture.This was done by comparing the experimental results of austenitic steel specimens with a strong variation in their stress triaxiality ratios. The specimens had cracks with varying depths and crack tip deformation modes; tension, in-plane shear, and out-of-plane shear. The crack growth in fracture mechanics specimens was compared with the failure of standard testing specimens for tension, upsetting and torsion. By associating the experimental results with finite element simulations it was possible to compare the critical plastic equivalent strain and stress triaxiality ratio values at fracture. In the investigated triaxiality regime an exponential dependency of the fracture locus on the stress triaxiality ratio was found.     

Buckling and postbuckling of anisotropic laminated cylindrical shells under combined axial compression and torsion

A postbuckling analysis is presented for an anisotropic laminated cylindrical shell of finite length subjected to combined loading of axial compression and torsion. The governing equations are based on classical shell theory with von Kármán–Donnell-type of kinematic nonlinearity and including the extension–twist, extension–flexural and flexural–twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine interactive buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, anisotropic laminated cylindrical shells for different values of load-proportional parameters. The results show that the postbuckling characteristics depend significantly upon the load-proportional parameter. The results reveal that in combined loading cases the postbuckling equilibrium path is unstable and the shell structure is imperfection-sensitive.     

Classes of exact solutions for buckling of multi-step non-uniform columns with an arbitrary number of cracks subjected to concentrated and distributed axial loads

The governing differential equation for buckling of a multi-step non-uniform column subjected to combined concentrated and distributed axial loads, each step of which has an arbitrary number of cracks with or without spring supports, is expressed in the form of bending moment. A model of massless rotational spring is adopted to describe the local flexibility induced by cracks in the column. In this paper, the distribution of flexural stiffness of a non-uniform column is arbitrary, and the distribution of axial forces acting on the column is expressed as a functional relation with the distribution of flexural stiffness and vice versa. The governing equation for buckling of a one-step non-uniform column is reduced to a differential equation of the second-order without the first-order derivative by means of functional transformation. Then, this kind of differential equation is reduced to Bessel equations and other solvable equations for six important cases. The exact buckling solutions of one-step non-uniform columns are thus found. Then a new approach that combines the exact buckling solution of a one-step column and the transfer matrix method is presented to establish the eigenvalue equation for buckling of a multi-step non-uniform column with spring supports. The main advantage of the proposed method is that the eigenvalue equation for buckling of a non-uniform column with an arbitrary number of cracks, any kind of two end supports and various spring supports at intermediate points can be conveniently determined from a second order determinant. Due to the decrease in the determinant’s order as compared with previously developed procedures the computational time required by the present method can be reduced significantly. A numerical example is given to examine the accuracy of the proposed method and to investigate the effect of cracks on buckling of a multi-step non-uniform column.     

The 3D stress field of a fiber embedded into a matrix and subjected to an axial load

In this investigation, the 3D stress field of a single cylindrical fiber, which is embedded into a plate matrix, is examined. The composite body is subjected to an axial loading and both perfect imperfect bonding conditions at the interface are considered. The analysis, which is based on analytical considerations, reveals the load transfer characteristics from the fiber to the matrix and vice versa. Numerical results for the displacement and stress fields are given and shown to be sensitive to the diameter to thickness ratio, the respective material properties and the applied load ratio between the fiber and the matrix. Comparisons with available experimental data shows a very good agreement.     

Thermal cycling response behavior of ceramic matrix composites under load and displacement constraints

Thermal cycling response of a two-dimensional carbon fiber reinforced SiC matrix composite (2D C/SiC) to load constraint (LC) and to displacement constraint (DC) in an oxidizing environment was investigated. During thermal cycling between 700 and 1200 °C, a constraint strain with a 0.208% range and a constraint stress with a 180 MPa range were, respectively, generated on the composites in LC and DC. It was found that with increasing cycles, the constraint strain increased in LC and the constraint stress decreased in DC. After 50 cycles, in contrast to the as-received composite materials, the as-cycled composites suffered greater loss in mechanical properties: the residual strength and failure strain are 204 MPa and 0.49% for the LC tested samples, and 223 MPa and 0.64% for the DC tested samples, respectively. Microstructural observations indicated that the LC could develop thermal microcracks and assist in oxidizing the internal fibers, whereas the DC reduced crack propagations and fiber oxidation because of decreasing tensile and increasing compressive stresses.     

Design of high-performing hybrid meta-heuristics for unrelated parallel machine scheduling with machine eligibility and precedence constraints

This study involves an unrelated parallel machine scheduling problem in which sequence-dependent set-up times, different release dates, machine eligibility and precedence constraints are considered to minimize total late works. A new mixed-integer programming model is presented and two efficient hybrid meta-heuristics, genetic algorithm and ant colony optimization, combined with the acceptance strategy of the simulated annealing algorithm (Metropolis acceptance rule), are proposed to solve this problem. Manifestly, the precedence constraints greatly increase the complexity of the scheduling problem to generate feasible solutions, especially in a parallel machine environment. In this research, a new corrective algorithm is proposed to obtain the feasibility in all stages of the algorithms. The performance of the proposed algorithms is evaluated in numerical examples. The results indicate that the suggested hybrid ant colony optimization statistically outperformed the proposed hybrid genetic algorithm in solving large-size test problems.     

Minimum surcharge load of URM walls under flexure and axial force / Mindestauflast bei Biegung mit Normalkraft

This paper suggests a detailed parametric study, which has been drawn up in connection with the question of the necessity of verification of masonry wall by a minimum vertical load subject to bending and normal force by the author and his team [7]. It assumes the actual eccentricities from supporting due floors and takes into account the second order theory in middle of wall according to DIN EN 1996‐1‐1 or the German NA. In some cases, the model is derived for very high wind loads to its limits. Using the arch model which is introduced in DIN EN 1996‐1‐1 and may be applied by NA, is helpful and effective. This method may provide higher capacity rather than for example, with the bar or plate model. In this article the verification by means of the arch model will be presented and discussed. It is also shown that, forming an arch opposing to the horizontal wind load and low vertical loads may not come to a stability failure.     

变温热源不可逆布雷顿制冷循环制冷率和制冷系数优化

用有限时间热力学方法分析变温热源不可逆简单布雷顿制冷循环的特性,分别以制冷率和制冷系数为优化目标,优化了循环中换热器的热导分配以及工质和热源间的热容率匹配,并采用数值计算分析了压比、换热器总热导、压缩机和膨胀机效率、工质热容率等参数对最优制冷率和制冷系数的影响特点.所得结果对工程制冷系统设计有一定的指导意义.     

Influences of elastic foundations and shear deformations on the buckling behavior of functionally graded material truncated conical shells under axial compression

This article presents an investigation on the buckling of functionally graded (FG) truncated conical shells under an axial load resting on elastic foundations within the shear deformation theory (SDT). The governing equations are solved using the Galerkin method, and the closed-form solution of the axial buckling load for FG conical shells on elastic foundations within the SDT is obtained. Various numerical examples are presented and discussed to verify the accuracy of the closed-form solution in predicting dimensionless buckling loads for FG conical shells on the Winkler–Pasternak elastic foundations within the SDT.     

Long-term stress relaxation behaviors and mechanisms of 2219 Al-Cu alloy under various temperatures and initial stresses

Large 2219 Al-Cu alloy aerospace integral components suffer from long-term stress relaxation aging(SRA)due to complex temperature and stress loads during aging treatment/forming and service process,which makes it difficult to ensure their appropriate residual stress and excellent mechanical and service prop-erties.However,the research is limited to a thorough understanding of macroscopic and microscopic features and underlying mechanisms of the long-term SRA under multivariable aging conditions.There-fore,this study investigated macroscopic and microscopic features of long-term SRA under different tem-peratures(120 ℃ to 190 ℃),initial stress levels(100 MPa to 250 MPa)and durations(0 h to 50 h)through stress relaxation curves,metallographic traits,Vickers hardness,tensile performance,disloca-tions and phases of precipitation.On the basis of experimental outcomes,the comprehensive mecha-nisms beneath SRA were unraveled through dislocation theory,multiphase strengthening mechanisms and thermodynamics,where the interplays of stress relaxation behavior with age-hardening response were taken into consideration.The results showed elevations in the rate of stress reduction as the tem-perature and initial stress rose.At an initial stress greater than the yield stress of alloy,a marked in-crease in stress relaxation was found,and the mechanisms transform from the intragranular motion of dislocations and diffusion of grain boundaries to the intragranular and intergranular motion of disloca-tions and migration of grain boundaries.The stress reduction rate rose sharply when the temperature exceeded 175 ℃,and the dislocation movement mechanisms transform from gliding to climbing of dislo-cations.Stress relaxation is in nature progressive transformation of strain from elastic into a permanently inelastic state via the motion of dislocations,leading to the decrease of movable dislocations and the increase of immovable dislocations with more stable configurations.The age hardening is mainly deter-mined by precipitation strengthening,supplementarily by dislocation strengthening,and obvious stress orientation effect(SOE)of G.P.zones and θ\"phases degenerates strengthening effect.The interplay be-tween stress relaxation behavior and age-hardening response influences the thermal-mechanical coupling SRA of 2219 Al-Cu alloy,which depends fundamentally on the motion of dislocations and their interplay with precipitated phases.This is a thermal activation process concerning the interplay between internal(age-hardening resistance)stress and external(initial)stress.The initial energy of elastic strain offers Gibbs free energy as the SRA driver,and a steady state of stress relaxation is attained with the lowest energy of elastic strain.These findings provide valuable insights into exploring innovative aging treat-ment/forming for optimizing residual stress,mechanical performance and service property in a synergistic manner.