Nonlinear Deformation Analysis Research Articles

Stretching and folding analysis of fluid based on covariance method

Fluid in a turbulent state will be continuously stretched and folded, and the boundaries of fluid elements will grow exponentially, leading to an intense mixing process between different regions. However, most studies focus on the fluid’s stretching process, and the definition of folding still needs to be clarified. In this paper, the covariance method is extended to study the nonlinear deformation of fluid. First, particle sets are used to characterize the fluid elements, and the evolution of particle sets could reflect the deformation process of fluid. Then, the stretching and folding degrees of fluid are defined based on the statistical parameters of the particle sets. Finally, the extended covariance method is applied to the double gyre and the flow around the square cylinder, and the results show that the stretching process dominates the early stage of fluid deformation, and the fluid in high stretching regions has a higher probability of folding. Importantly, the nonlinear stretching regions with high non-affine deformation-low folding properties are identified, and the spurious folding caused by nonlinear stretching is eliminated. In summary, the extended covariance method shows great potential in the nonlinear deformation analysis of fluid, contributing to a deeper understanding of transport and mixing.

Comparative analysis of the stability and natural vibrations of shallow panels under the action of thermomechanical loads

The work is a continuation of research devoted to substantiating the reliability of solutions obtained by the finite element method for the analysis of nonlinear deformation, buckling and vibrations of thin elastic shells under the action of thermomechanical loads. The method is based on geometrically nonlinear relations of the three-dimensional theory of thermoelasticity and the principles of the moment finite element scheme. A thin elastic shell of an inhomogeneous structure is modeled by a universal spatial isoparametric finite element. The modal analysis of the shell is implemented at each step of the static thermomechanical load. The subspace iteration method is used to determine the spectrum of the lowest frequencies of natural vibrations of shells. A shallow spherical panel with a square plan is considered. The effect of preheating on the loss of stability and vibrations of an elastic isotropic shell under uniform pressure loading is investigated. The behavior of the shell weakened by two pairs of cross-channels is analyzed. The weakening of the panel by narrow and wide channels, which can be eccentrically located relative to the middle surface of the shell, is considered. The effectiveness and adequacy of the method is confirmed by a comparative analysis of solutions with results obtained using modern multifunctional software systems LIRA-SAPR and SCAD. The features of using the systems for solving the problems under consideration are given. Analysis of the results made it possible to evaluate the possibilities of using these software systems to substantiate the reliability of solutions to certain classes of problems of geometrically nonlinear deformation, buckling and vibrations of elastic shells.

Modeling large-deformation features of the Lower San Fernando Dam failure with the Material Point Method

The Material Point Method (MPM) is used to model the well-known case study of the earthquake-induced Lower San Fernando Dam failure. This upstream flow slide, leaving only 1–2 m freeboard, emphasized the importance of seismic hazard analyses of earthen dams. This study expands on the Chowdhury (2019) nonlinear seismic deformation analysis, which successfully captured liquefaction initiation and engineering failure characteristics. It could not, however, fully capture the large-deformation behavior and post-failure equilibrium cross-section due to mesh entanglement limitations of the Finite Difference Method. This MPM model initializes post-shaking and simulates the large-deformation undrained behavior of both liquefied sands and shear-softened clays. Several novel features implemented in the MPM advance modeling capabilities, including a nonconforming traction boundary to model reservoir pressure, and an adhesion boundary to model the reservoir bottom sliding interface. Compared to previous studies, the current study predicts improved kinematic behavior and post-failure cross-sectional features. Qualitative highlights include well-defined shear banding, sharp heel scarp features, blocky features, a toe bulge, and shear separation of the leading slide mass. Quantitative highlights include 1.5 m remaining freeboard, 20 m crest loss, and 66 m upstream toe runout, versus field observations of 1.2–1.8, 20, and 65 m, respectively.

Nonlinear deformation analysis of magneto-electro-elastic nanobeams resting on elastic foundation by using nonlocal modified couple stress theory

This article investigates a comprehensive analysis of the bending problem pertaining to magneto-electro-elastic (MEE) nanobeams on the Winkler-Pasternak foundation. Taken into account the influence of size effects of nano structures, a non-classical mechanical model is established to describe the bending behavior for MEE nanobeams. In this research, the nonlocal modified couple stress theory is utilized to accurately capture both the softening and hardening effects resulting from the size effect. The theory of third-order shear deformation and von Karman geometric nonlinear theory are employed in conjunction with the introduction of Maxwell's equation to develop the model of MEE nanobeam, the control equation of the nonlinear bending problem of MEE nanobeams is obtained by Minimum potential energy principle, and it is solved by Galerkin method. Finally, this study provides a detailed discussion on the influences of the ratio of nonlocal parameters and length-scale parameters, Winkler-Pasternak coefficient, external magnetic potential, external voltage and span-thickness ratio on nonlinear deflection of nanobeam.

A Method for Analysis of Nonlinear Deformation, Buckling, and Vibrations of Thin Elastic Shells with Inhomogeneous Structures

The formulation of the problem and the method of analysis of the stress-strain state, buckling and vibrations of elastic shells with inhomogeneous structure are considered. The modal analysis of the shells is performed at each stage of loading. The method allows one to study the behavior of shells with a complex shape of the middle surface, geometric features throughout the thickness, and a multilayer material structure under thermomechanical loading. We approximate a thin shell with one finite element (FE) over the entire thickness. At the same time, we use spatial FEs of the same type to model shell portions with stepwise-varying thickness. So we apply the universal finite element. It is based on an isoparametric 3D element with polylinear shape functions for coordinates and displacements and has additional parameters. The universal finite element can be transformed (modified) to accurately describe portions of the shell with stepped-variable thickness. This element can be eccentrically displaced relative to the average surface of the shell and change its own thickness. The side edges of neighboring FEs are in continuous contact, and the FE allows simulating sharp bends of the shell. The approach is modern and easy to implement, since it is based on the use of the relations of the three-dimensional geometrically nonlinear theory of thermoelasticity and the application of the moment finite-element scheme. The effectiveness of the method is demonstrated on classical test examples. The convergence, accuracy and reliability of the obtained solutions are investigated. Comparison of the results of calculations obtained by the moment finite-element scheme with the data of other authors shows a good agreement between the solutions.

An extended ordinary state-based peridynamic model for nonlinear deformation and fracture

Peridynamic is a promising nonlocal continuum theory that reconstructs the equations of motion of solid mechanics using spatial integral equations, rendering it suitable for describing objects with discontinuities such as cracks. In this study, a novel extended ordinary state-based peridynamic model was developed for nonlinear deformation and fracture analysis, which established a general relationship with continuum-based parameters and permitted the selection of different influence functions. Based on the principle of virtual displacement, the complete derivations of the peridynamic parameters were presented for two and three-dimensional conditions. After that, the specific numerical scheme and algorithm implementation were summarized. The capability and accuracy of the proposed nonlinear model were verified by comparing with the experimental and finite element simulation results. Finally, several other numerical examples were provided to further demonstrate the applicability and robustness of the proposed model and its implementation.

Pipeline element for upheaval buckling analysis of submarine pipelines with geometric-imperfections under high temperature high pressure

Submarine pipeline is used for transporting oil from wells to resource storage facilities. The oil inside the pipeline is heated and pressured for long-distance transportation, making the pipeline under high temperature and high pressure (HTHP). The pipeline is usually placed inside a trench where surrounding soil restraints its longitudinal expansion. The pipeline is not perfectly straight, but with geometric imperfections, so the upheaval buckling may be triggered when the accumulated compression force has reached its buckling strength. It is not easy to conduct a geometrically nonlinear analysis for the pipeline because of the nonlinear soil–pipeline interactions (SPIs). This paper proposes a new line element aiming for the geometrically nonlinear large deformation analysis of the pipeline under HTHP. The axial expansion force due to high working temperature and pressure is included in the element formulation. Furthermore, a Gauss–Legendre integral method is employed to consider continuously distributed nonlinear SPIs in both lateral and longitudinal directions. Since the pipeline might exhibit large deflections, the analysis adopts the Updated-Lagrangian approach to establish the equilibrium conditions. A Newton–Raphson procedure is developed to execute the analysis. Detailed element formulations are given. Six groups of examples are provided to examine the robustness of the numerical method.

Nonlinear elastic deformation of Mindlin torus

The nonlinear deformation and stress analysis of a circular torus is a difficult undertaking due to its complicated topology and the variation of the Gauss curvature. A nonlinear deformation (only one term in strain is omitted) of Mindlin torus was formulated in terms of the generalized displacement, and a general Maple code was written for numerical simulations. Numerical investigations show that the results obtained by nonlinear Mindlin, linear Mindlin, nonlinear Kirchhoff–Love, and linear Kirchhoff–Love models are close to each other. The study further reveals that the linear Kirchhoff–Love modeling of the circular torus gives good accuracy and provides assurance that the nonlinear deformation and stress analysis (not dynamics) of a Mindlin torus can be replaced by a simpler formulation, such as a linear Kirchhoff–Love theory of the torus, which has not been reported in the literature.

Comparative Analysis of Nonlinear Deformation and Buckling of Thin Elastic Shells of Step-Variable Thickness

A comparative analysis of finite element models and methods for solving complex problems of geometrically nonlinear deformation, buckling and post-buckling behavior of thin shells of stepwise variable thickness is carried out. An approach based on the use of the moment scheme of finite elements is considered. The features of using the software suite LIRA and integrated software system SCAD for solving the assigned problems are also provided. Thin and medium thickness shells are considered. They can have different geometric features in thickness and be under the action of static thermomechanical loads. A technique for solving these problems with the help of an efficient refined approach is presented. The technique is based on the general methodological positions of the three-dimensional theory of thermoelasticity and the use of the finite element moment scheme. With this approach, the approximation through the shell thickness is carried out by a single universal spatial finite element. The element can be modified in different portions of the shell with a step-variable thickness. It can be located eccentrically relative to the middle surface of the casing and can change its dimensions in the direction of the shell thickness. Such a unified approach made it possible to create a unified designed finite element model of a shell of an inhomogeneous geometric structure under the combined action of a thermomechanical load. A comparative analysis of the application of three finite element approaches for problems of geometrically nonlinear deformation and buckling of shells of stepwise variable thickness is carried out.

Large-deformation mechanics of anti-curvature lattice materials for mode-dependent enhancement of non-linear shear modulus

Shear modulus assumes an important role in characterizing the applicability of different materials in various multi-functional systems and devices, such as deformation under shear and torsional modes and vibrational behavior involving torsion, wrinkling, and rippling effects. Lattice-based artificial microstructures have been receiving significant attention from the scientific community over the past decade due to the possibility of developing materials with tailored multifunctional capabilities that are not achievable in naturally occurring materials. In general, the lattice materials can be conceptualized as a network of beams with different periodic architectures, wherein the common practice is to adopt initially straight beams. While shear modulus and multiple other mechanical properties can be simultaneously modulated by adopting an appropriate network architecture in the conventional periodic lattices, the prospect of on-demand global specific stiffness and flexibility modulation has become rather saturated lately due to intense investigation in this field. Thus there exists a strong rationale for innovative design at a more elementary level in order to break the conventional bounds of specific stiffness that can be obtained only by lattice-level geometries. In this article, we propose a novel concept of anti-curvature in the design of lattice materials, which reveals a dramatic capability in terms of enhancing shear modulus in the nonlinear regime while keeping the relative density unaltered. A semi-analytical bottom-up framework is developed for estimating effective shear modulus of honeycomb lattices with the anti-curvature effect in cell walls considering geometric nonlinearity under large deformation. We propose to consider the complementary deformed shapes of cell walls of honeycomb lattices under anti-clockwise or clockwise modes of shear stress as the initial beam-level elementary configuration. A substantially increased resistance against deformation can be realized when such a lattice is subjected to the opposite mode of shear stress, leading to increased effective shear modulus. Within the framework of a unit cell based approach, initially curved lattice cell walls are modeled as programmed curved beams under large deformation. The combined effect of bending, stretching, and shear deformation is considered in the framework of Reddy’s third order shear deformation theory in a body embedded curvilinear frame. Governing equation of the elementary beam problem is derived using variational energy principle based Ritz method. In addition to application-specific design and enhancement of shear modulus, unlike conventional materials, we demonstrate through numerical results that it is possible to achieve non-invariant shear modulus under anti-clockwise and clockwise modes of shear stress. The developed physically insightful semi-analytical model captures nonlinearity in shear modulus as a function of the degree of anti-curvature and applied shear stress along with conventional parameters related to unit cell geometry and intrinsic material property. The concept of anti-curvature in lattices would introduce novel exploitable dimensions in mode-dependent effective shear modulus modulation, leading to an expanded design space including more generic scopes of nonlinear large deformation analysis.

Mean dilatational based finite element formulation for a nearly incompressible nonlinear large deformation analysis

Mean dilatational based finite element formulation for a nearly incompressible nonlinear large deformation analysis

Coupled peridynamic model for geometrically nonlinear deformation and fracture analysis of slender beam structures

AbstractSlender beam structures can experience large displacements, large rotations and fractures, even if the structures are only subjected to small loads. A coupling model of peridynamics (PD) and classical continuum mechanics (CCM) for beam fracture analysis in geometrically nonlinear deformations is developed in this study. Firstly, the formulations of virtually nonlinear strain energy density of each incremental step are obtained by using the updated Lagrangian (UL) formulation and von Karman beam theory, then the nonlinear PD beam parameters are established on the geometrically nonlinear micro‐beam bonds via the principle of virtual work and homogenization. Secondly, the coupling model of PD and CCM for geometrically nonlinear beams is proposed, for which the morphing method is applied to create a balance between the stiffness of geometrically nonlinear CCM beam model and the weighted coefficients of geometrically nonlinear PD beam model. Thirdly, a new fracture criterion for PD beam models considering the effect of geometrical nonlinearity is adopted. Finally, the large deformation and fracture analysis of straight beam, spiral slender beam and complex frame subjected to different loading conditions illustrate the validity and accuracy of the proposed PD‐CCM coupling model.

Nonlinear Deformation Analysis of Fg-Gpls Reinforced Asymmetric Sandwich Beams with Auxetic Core on Nonlinear Elastic Foundation Under Hygrothermal Conditions

Nonlinear Deformation Analysis of Fg-Gpls Reinforced Asymmetric Sandwich Beams with Auxetic Core on Nonlinear Elastic Foundation Under Hygrothermal Conditions

Anti-curvature honeycomb lattices for mode-dependent enhancement of nonlinear elastic properties under large deformation

Lattice-based artificial microstructures have been receiving significant attention from the scientific community over the past decade due to the possibility of developing materials with tailored multifunctional capabilities that are not achievable in naturally occurring materials. Such lattice materials can be conceptualized as a network of beams with different periodic architectures, wherein the common practice is to adopt straight beams. While a large set of mechanical properties can be simultaneously modulated by adopting an appropriate network architecture in the conventional periodic lattices, the prospect of on-demand global specific stiffness and flexibility modulation has become rather saturated lately due to intense investigation in this field. Thus there exists a strong rationale for innovative design at a more elementary level in order to break the conventional bounds of specific stiffness that can be obtained only by lattice-level geometries. Here we propose a novel concept of anti-curvature in the design of lattice materials, which reveals a dramatic capability in terms of enhancing the effective elastic moduli in the nonlinear regime while keeping the relative density unaltered. A semi-analytical bottom-up framework is developed for estimating effective elastic moduli of honeycomb lattices with the anti-curvature effect in cell walls considering geometric nonlinearity under large deformation. We propose to consider the deformed shapes corresponding to compressive or tensile modes of the honeycomb cell walls as the initial beam-level configuration. A substantially increased resistance against deformation can be realized when such a lattice is subjected to the opposite mode, leading to increased effective elastic moduli. Moreover, unlike conventional materials, we demonstrate that it is possible to achieve non-invariant elastic moduli under tension and compression. Within the framework of a unit cell based approach, the cell walls with initial curvature are modeled as curved beams including nonlinear bending and axial deformation, wherein the governing equation is derived using variational energy principle through the Ritz method. The developed physically insightful semi-analytical model captures nonlinearity in elastic moduli as a function of the degree of anti-curvature and applied stress along with conventional parameters related to unit cell geometry and intrinsic material property. The concept of anti-curvature in lattice materials proposed in the present article introduces novel exploitable dimensions in mode-dependent effective elastic property modulation, leading to an expanded design space including more generic scopes of nonlinear large deformation analysis.

Finite element analysis of nonlinear deformation, stability and vibrations of elastic thin-walled structures

Thin-walled shell-type structures are widely used in various branches of technology and industry. Such structures under operating conditions are usually exposed to various loads, including thermomechanical ones. Real shell structures, as a rule, have a complex shapes. To increase reliability, reduce material consumption, for technological reasons, they are designed as inhomogeneous systems in thickness. This causes a great and constant interest of engineers and designers in the problems of investigating the behavior of elastic thin-walled shell structures.
 The work is devoted to the method of analysis of geometrically nonlinear deformation, stability, post-buckling behavior and natural vibrations of thin elastic shells of complex shape and structure under the action of static thermomechanical loads. The unified design model has been created on the basis of the developed universal spatial finite element with introduced additional variable parameters. The model takes into account the multilayer material structure and geometric features for structural elements of the thin shell. The shells can be reinforced with ribs and cover plates, weakened by cavities, channels and holes, have sharp bends in the mid-surface.
 Such a uniform formulation made it possible to create a unified finite element model of the shells with an inhomogeneous structure. It is shown on a number of problems that the method presented in this article is an effective tool for analyzing geometrically nonlinear deformation, stability, post-buckling behavior and natural vibrations of thin elastic shells of an inhomogeneous structure under the action of static thermomechanical loads.

The simplified analysis method of nonlinear buckling and displacement of latticed structure

In order to simplify the modeling process of building complex lattice structures by finite element analysis software, a simplified method for nonlinear buckling and deformation analysis of lattice structures based on equivalent inertia moment method is proposed. By comparison with the displacements, the latticed structure is equivalent to a solid structure, and the expression of the equivalent inertia moment of a typical latticed structure is given. The finite element analysis software ANSYS is used to analyze the buckling problem and the deformation of latticed structure and the equivalent solid structure, furthermore, the load-displacement curves of the actual structure and equivalent model are obtained. The results show that the simplified analysis method of nonlinear buckling and deformation of latticed structure is feasible and can satisfy the needs of engineering design.

Nonlinear deformation analysis of compressed reinforced concrete elements of circular cross-section

Nonlinear deformation analysis of compressed reinforced concrete elements of circular cross-section

On deformation criteria of a special limit state of eccentrically compressed elements of RC building frames

At accidental impacts caused by the sudden removal of a load-bearing element of the building frame, the stress-strain state of the sections of eccentrically compressed structural elements such as columns, pylons, braces and belts of trusses, etc. becomes more disadvantageous than their stress-strain state at the stage of normal operation. The factors that lead to such a situation are sharp increase in the eccentricities of loads attaching, slenderness of cross sections, corrosion, initial curvature and mechanical damages. In these cases, buckling scenario for the exhaustion of their bearing capacity is a possible scenario. The paper proposes an approach to the obtaining of deformation criteria for assessing the special limiting state of eccentrically compressed bar elements of reinforced concrete frames. Such an approach is based on the use of a combination of nonlinear deformation analysis and nonlinear stability analysis. Paper shows that the limiting values of deformations for the considered reinforced concrete element can be determined by the criteria of strength or buckling, depending on the ratio of the forces acting in the sections of the structural element.

Nonlinear dynamic response and deformation analysis of soil under the explosion shock loading

Energy is released during explosions, and this creates shock waves. The dynamic pressure generated from an explosion is transmitted through soil in the form of compression waves. In military engineering and industrial safety protection, soil, a blast-resistant material, is used to achieve blast resistance. This study used the blast pressure and ground acceleration measured in an experimental explosion to verify the results of finite element numerical analysis. A fluid–solid interaction numerical analysis method was employed to simulate a trinitrotoluene explosion on the ground. Through analysis of the dynamic characteristics of soil after an explosion, the relationship between the dynamic stress wave formed by the explosion and the plastic deformation of the soil was studied. The results may provide a reference for the design of blast-resistant protective soil layers.

Nonlinear stress and deformation analysis of pressurized thick-walled hyperelastic cylinders with experimental verifications and material identifications

The main purpose of the present research is the investigation of the stress and displacement distributions of the internally pressurized thick-walled hyperelastic cylindrical vessels or pressure pipes. The governing equations are derived by incorporation of the incompressible neo-Hookean and Mooney-Rivlin hyperelastic constitutive models into the direct hyperelasticity theory in the von Karman framework of large deformations. In contrast to all the available researches, no simplifications or linearization are made. The non-linear governing equations are solved by utilizing a second-order point-collocation procedure and implementation of details of the proposed incremental iterative solution scheme in the Matlab code written by the authors. Another novelty of the present research is experimentally identifying the employed polymeric hyperelastic material and verification of the results through experiments conducted by the authors. Due to using both nonlinear constitutive laws and nonlinear stress-displacement relations, through-thickness distributions of the radial displacement and radial and circumferential stresses are extracted for various pressures. The experimental results reveal that while the neo-Hookean hyperelastic model cannot be used for materials with stress-softening, the Mooney-Rivlin model reproduces the experimental results with excellent accuracy. In addition to the experimental verification, the results are verified by the Abaqus finite element analysis code as well.