Minimum Strain Energy Research Articles

Application of adaptive grid-based multi-objective particle swarm optimization algorithm for directional drilling trajectory design

The parameters optimization is the key issue for directional drilling trajectory design in oil and gas fields development, and there are three main challenges in multi-objective and multi-constraint optimization: (1) how to establish a multi-objective optimization model based on geological constraints; (2) how to design an appropriate optimization algorithm and solve the optimization model effectively; (3) how to select the desired result from the obtained Pareto solution and meet the engineering requirements. To build a safe and cost-efficient directional drilling trajectory, a new multi-objective optimization model is established in this paper. The effective objective functions to evaluate the drilling trajectory are summarized as the minimum trajectory length, torque, and strain energy. Moreover, the new model takes the wellbore stability based on Mohr–Coulomb criterion as constraint to prevent the borehole from collapsing. A novel adaptive grid-based multi-objective particle swarm optimization(AGMOPSO) is presented to achieve a set of Pareto optimal solutions of the established optimization model. In this algorithm, a new particle flight mode based on arcsine function of inertia weight and Gaussian mutation strategy are introduced to further improve the global searching ability and obtain more non-inferior solutions. To ensure the uniformity of non-inferior solutions, the adaptive grid based on density control factor is designed to map the space of objective functions to the grid space and adaptively adjust the density of non-inferior solutions in the external archive. Besides, a linear weighted summation function is developed to realize leader selection and archive maintenance of non-inferior solutions. The optimization results on the Pareto front indicate that AGMOPSO has better convergence and uniformity than the unmodified algorithm and reported results. To be concluded, AGMOPSO achieves a better optimization performance and obtain a better trajectory for drilling trajectory optimization model with geological constraints, which has good practical and theoretical significance for directional drilling trajectory optimization.

A comprehensive study on the influence of T-stress term on crack initiation angle in orthotropic materials based on the modification of MTS, MSS, SER and SED criteria

Theoretical predictions using conventional fracture criteria indicate that the theoretical approaches are not compatible with the experimental data. The most important reasons for the inconsistency between theoretical criteria and experimental data are lack of attention to accurate prediction of the crack initiation angle in fracture phenomenon and the role of T-stress term in the theoretical analysis. In available theoretical criteria, the fracture behavior of orthotropic materials was studied roughly considering crack initiation angle in the fiber direction. In this way, the accurate prediction of this angle has a significant impact on the extraction of the fracture limit curve consistent with experimental data. In the presented work, a comprehensive study on the role of the T-stress term on the fracture assessment of orthotropic materials based on the maximum strain energy release rate, minimum strain energy density, maximum tangential stress, and maximum shear stress criteria is performed. These criteria can characterize the mechanism of crack initiation under mixed-mode I/II loading and consider the effect of the T-stress term on the crack initiation angle. The formulations of the presented criteria for orthotropic materials are developed using the orthotropic stress field. Based on these criteria, the crack initiation angle is extracted in each mode mixity and the effect of the T-stress term on crack initiation angle is studied. A new approach is used to derive the T-stress term. The results indicate that by crossing pure mode I and approaching pure mode II, the T-stress term has a remarkable influence on the crack initiation angle and fracture assessment of orthotropic materials. Also, based on these criteria, FLC’s are extracted for orthotropic materials and the influence of this stress on crack behavior is evaluated. To verify the proposed formulations of these criteria, the fracture behavior based on the presented criteria is compared with the available experimental data and the accuracy of proposed theoretical approaches is discussed. It reveals that the presented criteria reliably estimate crack initiation angle and the crack behavior more accurately than the conventional fracture criteria for orthotropic materials.

Topology Optimization of Stiffener Layout Design for Box Type Load-Bearing Component under Thermo-Mechanical Coupling

The structure optimization design under thermo-mechanical coupling is a difficult problem in the topology optimization field. An adaptive growth algorithm has become a more effective approach for structural topology optimization. This paper proposed a topology optimization method by an adaptive growth algorithm for the stiffener layout design of box type load-bearing components under thermo-mechanical coupling. Based on the stiffness diffusion theory, both the load stiffness matrix and the heat conduction stiffness matrix of the stiffener are spread at the same time to make sure the stiffener grows freely and obtain an optimal stiffener layout design. Meanwhile, the objectives of optimization are the minimization of strain energy and thermal compliance of the whole structure, and thermo-mechanical coupling is considered. Numerical studies for square shells clearly show the effectiveness of the proposed method for stiffener layout optimization under thermo-mechanical coupling. Finally, the method is applied to optimize the stiffener layout of box type load-bearing component of the machining center. The optimization results show that both the structural deformation and temperature of the load-bearing component with the growth stiffener layout, which are optimized by the adaptive growth algorithm, are less than the stiffener layout of shape ‘#’ stiffener layout. It provides a new solution approach for stiffener layout optimization design of box type load-bearing components under thermo-mechanical coupling.

Morphogenesis of free-form surfaces by an effective approach based on isogeometric analysis and particle swarm optimization

In this paper, computer graphics, isogeometric analysis and structural optimization methods are combined to study the shape optimization of free-form surfaces. The free-form surface is modeled parametrically using NURBS techniques. The particle swarm optimization algorithm is used to optimize the surface shape, using the total strain energy of the structure as the objective function and the control point coordinates as the optimization variables, to find the reasonable surface form with the minimum strain energy. Three examples are considered to highlight the accuracy and effectiveness of the developed method.

Strut-and-tie model applications on reinforced concrete deep beam: A comprehensive review

Strut-and-tie model (STM) is the most important advance in designing complex prestressed and reinforced concrete structures. However, selecting a proper STM for reinforced concrete deep beams is still a challenging task for engineers and designers due to the complex shear behavior of such deep members. This article provides a review on the STM and its applications that are existing in the open literature. Accordingly, a review of the STM technique is presented with a particular focus on the basic concept of STM, associated B- and D-regions, STM elements, STM historical development, and STM applications in RC deep beams. The review also covers a wide range of STM aspects including: strut strength and its effectiveness factor, node strength and its effectiveness factor, tie strength and minimum reinforcement, the effect of tie anchorage, and strain energy minimization. Hence, essential formulas and parameters of STM proposed by various design codes and researchers are reviewed and then summarized in comprehensive tables. Consequently, from the reviewed literature, several challenges are identified and some recommendations that are necessary to be considered in future works are addressed. With the provided information, this review article serves as a useful reference for structural engineers and researchers who are familiar with STM, as well as who wish to enter this research field.

Experimental and theoretical investigation of mixed-mode I/II and I/III fracture behavior of PUR foams using a novel strain-based criterion

Brittle fracture in Polyurethane (PUR) foam is experimentally and theoretically investigated under mixed-mode I/II and I/III loading conditions. Original test data are generated to examine different criteria in prediction of the mixed-mode fracture behavior of PUR foam. To this end, edge notched disc bend (ENDB) specimen which has been proven to be a suitable test configuration for such loading conditions is used, and subsequently, fracture angles and fracture toughness values are obtained experimentally. Three different fracture criteria, including minimum strain energy density (SED), maximum principal stress (MPS), and the recently introduced strain-based criterion called ECD-SN – which is established based on considering an effective critical distance – are considered to theoretically estimate the fracture behavior of PUR foam. A comparison between the experimental and theoretical results revealed that the ECD-SN criterion gives a better prediction both for the fracture angles and the mixed-mode fracture toughness of PUR foam. The results indicated that considering effective critical distance instead of the traditional approach, which assumes the critical distance is constant as a material property and independent of the loading mode, can considerably increase the accuracy of the theoretical estimation.

Investigation of the potential of topology optimization in additive manufacturing using the example of components subject to bending stress

AbstractIn this application‐oriented work, we examine the performance of topology‐optimized structures as compared to the reference I‐beam. We make use of the thermodynamic topology optimization based on a linear elastic compliance minimization, i. e. minimization of the elastic strain energy of the whole structure. We investigate, how the optimization of the rather theoretical strain energy influences the efficiency of more practical measurements, i. e. the force‐displacement response at the loading points and the maximum tolerable force. For this purpose, starting from a cuboid design space with the boundary conditions of a 3‐point and 4‐point bending stress, the geometry with constant volume was optimized. The topology‐optimized bending beams were subsequently produced by stereolithography and mechanically tested with respect to the previously defined boundary conditions. In order to avoid a falsification of results due to internal sample defects, all samples were previously examined with the aid of computer tomography with regard to the defects in the volume. As a general result, the topology‐optimized bending beams can bear a higher load in the experiment, which shows the usefulness of the coupling of additive manufacturing and topology optimization methods without any special constraints or enhancements regarding the manufacturing process within the optimization.

A Continuum-mechanics solution of laminate free edges based on asymmetric stress and strain tensors

A meaningful attempt is made to investigate the impact of using asymmetric stress and strain formulations in the prediction of free-edge response of laminated orthotropic materials. The paper contributes to the process of making the singular free-edge stresses and strains in the literature more proximate to the bounded (realistic) solutions. Related to the singularity issue, it was previously identified that the symmetry assumption for stress and strain tensors could lead to a contradiction with the predicted free-edge stress functions. It is, therefore, reasonable to assert that the classical continuum mechanics based on tensor symmetries is unfaithful for the modelling of free edges. The present study demonstrates that for the free-edge region, stress and strain tensors naturally become asymmetric when they are enabled to be, to reach the minimum strain energy. By comparing with strain predictions generated by Digital Image Correlation technique, the new framework is shown to be able to address the notable discrepancy between the classical theoretical result and experimental result, which suggested the higher fidelity of the new framework. Moreover, by resolving the contradiction, the model is also made less sensitive to mesh refinement which sets an important basis for reaching a bounded solution in the future.

Applying the new experimental midpoint concept on strain energy density for fracture assessment of composite materials

A mixed-mode I/II fracture criterion for predicting the fracture response of composite materials is proposed. This criterion is derived based on a comprehensive study and the consideration of the physics of fracture onset. The fracture phenomenon that causes the various damage mechanisms at the vicinity of the crack tip is examined. It is elucidated that the stress distribution at the crack tip ought to be defined using the reinforcement isotropic solid (RIS) stress state. This new criterion, which is called Improved Strain Energy Density with Mid-point (ISEDM), includes the effect of the fracture process zone (FPZ) and T-stress, which remarkably affect the mixed-mode fracture process, particularly, when mode II is dominant. Substituting the strain energy density in a pure mode I with the strain energy density in the midpoint of mixed-mode I/II is the creative idea employed in proposing this criterion. Because in pure mode I the effects of FPZ are minimal, change of fitting point on fracture limit curve (FLC) from KIc to midpoint critical stress intensity factors (CSIF’s) makes it possible to consider the effects of FPZ more accurately. In the ISEDM criterion, fracture behavior depends on mechanical properties and CSIF’s of the midpoint. Crack initiation angle is considered along minimum strain energy density and this angle is derived in the midpoint of mixed-mode I/II. RIS theory is used as an applicable theory for modeling orthotropic materials in this paper and causes valid and reliable fracture behavior to be extracted. In addition, changing fracture point from pure mode I to the mid-point of experimental data causes the effects of FPZ to be considered without estimating the toughening mechanisms in this zone, and the fracture behavior is extracted with higher accuracy. FLC’s in comparison with available experimental data prove that the ISEDM criterion anticipates the fracture behavior of orthotropic materials well. Finding KIIc based on the analytical method is a valuable achievement. In this article, KIIc can be predicted with appropriate accuracy, only by CSIF’s of mid-point and using ISEDM criterion.

On the uniform torsional rigidity of square concrete-filled steel tubular (CFST) sections

There are a number of scenarios in which structural members experience torsion, including under the direct application of torsional loading, when transverse loading is applied at an eccentricity to the shear centre and as a second order effect arising from lateral torsional instability. To date, the torsional rigidity of concrete-filled steel tubular (CFST) sections has yet to be fully explored; hence a study into the uniform torsional rigidity of square CFST sections is presented herein. First, the strain energy of square CFST sections is formulated, in which the longitudinal warping displacement is assumed to have an undetermined constant. The undetermined constant is then deduced by means of the principle of minimum strain energy, and thus an analytical expression for the uniform torsional rigidity of square CFST sections is obtained. The accuracy of the derived formula is verified against existing theoretical solutions for simplified scenarios, test data and the results of numerical simulations. Finally, the influence of the key parameters in the derived formula for the torsional rigidity of square CFST sections are analysed, and a simplified design formula is presented.

Kinematic Chain Equivalent Method for Tube Model and Elastodynamic Optimization for Parallel Mechanism Based on Matrix Structural Analysis

The platforms of parallel mechanisms usually suffer vibration loads. In these cases, structure elastodynamic analysis and elastodynamic optimization of parallel mechanisms are important. A tube structure is very common for parallel mechanisms. This work establishes the model of a tube structure based on matrix structural analysis. The kinematic pair equivalent method is used to simulate the surface contact between the inner and outer tubes. The corresponding mass and stiffness matrices are derived through the strain energy minimization method. The reconfigurable legged lunar lander has been used as an example to verify the effectiveness of this method. By adding the mechanism configuration to the optimization process, the equivalent static load method and the desirability approach are combined and modified. A procedure for the multi-objective elastodynamic optimization of parallel mechanisms is proposed. The optimization procedure is implemented on the lander and the results show a reduction in mass and an increase in natural frequency.

Elastic interaction energy analysis during twin plane formation in the martensitic transformation process of α"-martensite in Ti-Nb-Al

To understand the twin selection mechanism that occurs in the initial stage of the martensitic transformation of shape memory alloys, the stress state during twin plane formation was numerically analyzed by micromechanics. The self-accommodation microstructure of α''-martensite of the Ti-23Nb-3Al (at%) shape memory alloy, in which the lattice parameter was adjusted to eliminate the formation of internal twinning due to lattice-invariant deformation, was adopted for analysis. The two lattice correspondence variants (CVi and CVj) formed a twin plane. CVi was assumed to be spheroid, and the elastic strain energy during twin plane formation was evaluated by analyzing the elastic interaction energy when CVj formed around CVi. There are three types of twins ({011}α" compound twin, {111}α" type I twin, and <211>α" type II twin) in the self-accommodation microstructure of α"-martensite. Regardless of the CVi geometry (i.e., aspect ratio (1 to 0.01) and minor axis orientation), the {111}α" type I twin exhibited minimum elastic interaction energy, indicating that minimum elastic strain energy was generated during this twin plane formation. This result is consistent with the experimental results, which showed the selective formation of {111}α" type I twins in the initial stage of martensitic transformation.

Analytical and experimental investigation on the effect of loading rate on the fracture toughness and fracture envelope in brittle rocks

Fracture toughness of brittle rocks is an essential factor for analyzing and designing many problems in rock mechanics such as crack initiation and propagation in rock masses, hydraulic fracturing, geothermal energy, etc. This parameter is closely related to the strain rate to which the rock mass is subjected. Therefore, the effect of strain rate on the fracture toughness under three loading modes (pure mode I, mixed mode loading I/II and pure mode II) by taking into account crack propagation speed was investigated in this work. Experiments were conducted on rectangular specimens of hornfels rock and two fracture criteria that include maximum tangential stress criterion (ϭ-criterion) and minimum strain energy density criterion (S-criterion) were adopted to verify their ability to predict the fracture envelope as a function of the strain rate. Results indicated that by increasing the strain rate from 6 × 10−4 to 6 × 10−2 S−1, fracture toughness under pure mode I, mixed mode loading I/II and pure mode II increased by 1.6, 1.8 and 1.9 orders of magnitudes, respectively. The fracture toughness under pure mode I and mixed mode loading I/II almost has the same increment rate versus strain rate (∼21). While the increment rate of the fracture toughness under pure mode II (∼37) is larger than that under pure mode I and mixed mode loading I/II. S-criterion indicated that by increasing the crack propagation speed, fracture envelope moves up and the fracture resistance for growth under mixed mode loading I/II increases. While for ϭ-criterion, two cases can be distinguished, for crack propagation speed less than 80% the Rayleigh wave speed, fracture envelope moves down by increasing the crack propagation speed, and the vice is versa for crack propagation speed greater than 80% of the Ryleigh wave speed. S-criterion is better than ϭ-criterion to characterize the fracture envelope under low strain rate, and for high strain rates, S-criterion should be developed to better characterize the fracture envelope.

Designing moulded pulp packaging using a topology optimization and superimpose method

AbstractMoulded pulp is a paper‐based packaging solution that is fully biodegradable and has been growing in demand due to environmental considerations. While demand has been growing, many moulded pulp packaging designs are based on the experience and knowledge of the package designer, which can lead to avoidable design issues. To solve this issue, this paper introduces a moulded pulp packaging design method using topology optimization. Topology optimization provides a systematic way to find the conceptual optimum design by minimizing strain energy. Taking the results of the topology optimization and implementing a superimpose method, the design process can be more efficient than the conventional design method. As a result, the proposed method provides a design that reduces the maximum stress of the packaging structure. With the reduction in stress, an exhaustive search method is then used to reduce the thickness of the package to decrease material usage while maintaining stress reduction.

ON ESTIMATING PLASTIC ZONES AND PROPAGATION ANGLES FOR MIXED MODE I/II CRACKS CONSIDERING FRACTAL EFFECT

This paper mainly investigated the influence of the fractal dimension of mixed mode I/II crack on its near-tip plastic zones and propagation angles. The near-tip distortional strain energy density for mixed mode I/II crack is modified by considering its fractal dimension. Using the Von Mises yield condition, the plastic zones at the fractal crack tip are evaluated. The effects of the fractal dimension of crack on the near-tip plastic zones are analyzed qualitatively. A modified criterion minimizes the fractal distortional strain energy density to predict the propagation direction of mixed mode I/II crack. Based on this, the effects of fractal dimension on the mixed mode I/II crack propagation direction at different inclination angles are discussed quantitatively. In addition, the modified criterion is compared to the experimental data in the literature, as well as the classical maximum tangential stress criterion and minimum strain energy density criterion. The results indicate that the fractal dimension of crack is an important factor in evaluating the crack-tip plastic zones and predicting the crack propagation angle, and the modified fractal criterion is more accurate and effective in predicting the crack propagation angles.

Optimization of the number and positions of fixture locators for curved thin-walled parts by whale optimization algorithm

Optimizing the fixture layout of the locating element is an important method to reduce the clamping deformation of thin-walled parts. A method for optimizing the fixture layout based on whale optimization algorithm is proposed in this paper, the number and positions of the fixtures for curved thin-walled parts are optimized. Firstly, the multi-point flexible locating tooling for curved thin-walled parts is developed based on the multi-point support technology. Then the strain energy is used to describe the deformation of the curved thin-walled parts in all directions, and an optimization model that takes the position of the locating element as a decision variable and minimum strain energy as the goal is established. Combined with the whale optimization algorithm and the parameterized finite element analysis, the optimal design of the number and positions of fixture locators for curved thin-walled parts are realized. Finally, the effectiveness of the proposed method is validated by the aircraft skin locating layout optimization, and a multi-point flexible locating and deformation measurement platform is constructed to verify the results of finite element calculations.

Multi-Material and Multiscale Topology Design Optimization of Thermoelastic Lattice Structures

This study establishes a multiscale and multi-material topology optimization model for thermoelastic lattice structures (TLSs) considering mechanical and thermal loading based on the Extended Multiscale Finite Element Method (EMsFEM). The corresponding multi-material and multiscale mathematical formulation have been established with minimizing strain energy and structural mass as the objective function and constraint, respectively. The Solid Isotropic Material with Penalization (SIMP) interpolation scheme has been adopted to realize micro-scale multi-material selection of truss microstructure. The modified volume preserving Heaviside function (VPHF) is utilized to obtain a clear 0/1 material of truss microstructure. Compared with the classic topology optimization of single-material TLSs, multi-material topology optimization can get a better structural design of the TLS. The effects of temperatures, size factor, and mass fraction on optimization results have been presented and discussed in the numerical examples.

Research on seismic ground motion parameters applicable to the safety of rectangular shallow tunnel

The objective of this paper is to optimize the selection of seismic ground motion intensity indexes in the seismic fortification of urban shallow-buried rectangular tunnels. This paper takes a shallow-buried rectangular tunnel in a city as the research object, uses ABAQUS to establish a finite-infinite element coupling model, and selects 70 typical seismic ground motions for dynamic calculation. Using dynamic time history analysis method to study the seismic response of tunnel lining structure in terms of internal force, minimum safety factor and strain energy, and analyze their correlation with 15 seismic ground motion parameters. Selecting the seismic ground motion parameters with strong correlation, good effectiveness, and high credibility for safety evaluation. The research results show that: Peak acceleration (PGA) has a weak correlation with the seismic response of tunnel lining structures, and PGA as an independent seismic ground motion intensity index has greater uncertainty in the seismic fortification of tunnels; Peak displacement (PGD), Root-mean-square velocity (RMSV), Root-mean-square displacement (RMSD), and Specific energy density (SED) can be used as independent seismic ground motion intensity index, The linear regression model is used to evaluate the safety of the lining structure, and finally the evaluation result is verified by the incremental dynamic analysis method (IDA), which shows that the evaluation result is accurate. The research results can provide reference for the preliminary design of seismic fortification of rectangular shallow tunnels.

Topology optimization analysis for minimization of strain energy using the modified optimality criteria method

Topology optimization analysis for minimization of strain energy using the modified optimality criteria method

Finite Element Analysis and Topology Optimization Design of Anchor Mooring Winch Support Bracket

The weight of the deck machinery greatly affects the position of the small ship’s center of gravity so that it also affects the stability of the ship. Therefore, it is necessary to conduct optimization studies to reduce the weight of ship deck machinery, especially anchor mooring winch, by reducing the weight of ship deck machinery will lower the position of the center of gravity of ship so that can improve ship stability. This paper presents the effects of a topology optimization examination based on the finite element evaluation on anchor mooring winch support bracket using the SolidWorks Simulation module. The main intention to examine is to optimize the general weight of the anchor mooring winch support bracket via way of means of thinning specific regions of the anchor mooring winch support bracket in keeping with the calculated minimum strain energy. The topology optimization algorithm that is used in the current study gives an optimal structural shape of the support bracket of the anchor mooring winch with the largest stiffness, considering the given quantity of mass so that it will be eliminated from the preliminary layout space. The complete sequence of steps for carrying out the topology control optimization study is shown, taking into account the constraints arising from the construction features and the method of manufacturing the support bracket of the anchor mooring winch. The layout became carried out, and the effects have been provided via way of means of evaluating the preliminary version and the optimized version. As the result of topology optimization study, its stress was increased by about 4MPa and mass was reduced by about 15kg in comparison with the initial design.