Linear Elastic Method Research Articles

Seismic Behavior Analysis of a 14th Century Anatolian Seljuk Kumbet

The preservation of cultural heritage and the seismic resilience of historic buildings are crucial for maintaining social identity, particularly in earthquake-prone regions. This study focuses on the modeling of Sırçalı Kumbet, a Seljuk monument built in the 14th century in Kayseri province, located in the Central Anatolia region of Turkey, using survey drawings and analysis using the finite element method (FEM) to evaluate its seismic performance. The analysis indicates that linear elastic calculation methods can serve as an initial approach for evaluating such geometrically complex structures. The findings demonstrate that Sırçalı Kumbet exhibits substantial structural rigidity, reducing deformation and enhancing resistance to material fatigue during seismic events. Displacement and stress analyses under G+EQx and G+EQy loading conditions reveal that tensile and compressive stresses remain within acceptable limits, with localized exceedances occurring at specific points, such as cavity corners and wall bases. While these localized stresses are manageable, they highlight areas that require continuous monitoring and potential reinforcement to ensure long-term stability. Additionally, the study suggests that the integration of regular maintenance and targeted reinforcement measures can further improve the monument’s durability and minimize potential damage. This research underscores the essential role of the FEM in bridging the gap between cultural heritage conservation and seismic resilience. It provides a methodological framework for integrating architectural, restoration, and engineering expertise into comprehensive conservation strategies. Future studies should expand this approach to include various building types and material properties to enhance the development of preservation strategies.

Study on bending performance of prefabricated glulam-cross laminated timber composite floor

Abstract The glulam-cross laminated timber (CLT) composite floor is a type of prefabricated composite floor that integrates glulam beams and CLT slab into a unified structure using shear connectors. To investigate the bending performance of the glulam-CLT composite floor, the bending test was conducted on a full-scale composite floor under static load. The study comprehensively analyzed the failure mechanism, load–deflection behavior, interface slip and strain distribution of the glulam-CLT composite floor. The test results of the composite floor indicated that the failure mode was tensile fracture of the wood beam at the bottom. As the load increased, the deflection deformation of the mid-span beam exceeded that of the edge beam. When the load reached its ultimate limit, the deflection deformation of the mid-span beam increased by 14.4% compared to the edge beam. In the early loading phase, the strain distribution of the composite section satisfied the assumption of a plane section. However, the strain distribution deviated from this assumption with the increased load due to the relative slips between the glulam beam and CLT flange. To calculate the bending performance of the composite floor, the M-shaped section of the glulam-CLT composite floor was simplified as T-section composite beams. The linear-elastic method for determining the flexural rigidity and ultimate bearing capacity of the glulam-CLT composite floors was proved to be accurate and reliable. The findings provided valuable insights into the bending behavior of the CLT flange under load and emphasized the non-uniform stress distribution caused by shear lag effects.

DCEM: A deep complementary energy method for linear elasticity

DCEM: A deep complementary energy method for linear elasticity

Solving linear elasticity benchmark problems via the overset improved element-free Galerkin-finite element method

A novel approach for the solution of linear elasticity problems is introduced in this communication, which uses a hybrid chimera-type technique based on both finite element and improved element-free Galerkin methods. The proposed overset improved element-free Galerkin-finite element method (Ov-IEFG-FEM) for linear elasticity uses the finite element method (FEM) throughout the entire problem geometry, whereas a fine distribution of overlapping nodes is used to perform higher order approximations via the improved element-free Galerkin (IEFG) technique in regions demanding more computational accuracy. The method relies on keeping the FEM-based results in those regions where low order of approximation is enough to provide the required accuracy, i.e. outside the region where the solution will be enriched via the IEFG technique. The overlapping domains perform an iterative transfer of kinematics information through well-defined immersed boundaries, and a detailed explanation on this regard is also presented in this communication. The Ov-IEFG-FEM is used in a set of increasingly complex linear elasticity problems, and the outcomes demonstrate the suitability and reliability of this technique to solve such problems in an accurate and remarkably simple manner.

Impact of stress regime change on the permeability of a naturally fractured carbonate buildup (Latemar, the Dolomites, northern Italy)

Abstract. Changing stress regimes control fracture network geometry and influence porosity and permeability in carbonate reservoirs. Using outcrop data analysis and a displacement-based linear elastic finite-element method, we investigate the impact of stress regime change on fracture network permeability. The model is based on fracture networks, specifically fracture substructures. The Latemar, predominantly affected by subsidence deformation and Alpine compression, is taken as an outcrop analogue for an isolated (Mesozoic) carbonate buildup with fracture-dominated permeability. We apply a novel strategy involving two compressive boundary loading conditions constrained by the study area's NW–SE and N–S stress directions. Stress-dependent heterogeneous apertures and effective permeability were computed in the 2D domain by (i) using the local stress state within the fracture substructure and (ii) running a single-phase flow analysis considering the fracture apertures in each fracture substructure. Our results show that the impact of the modelled far-field stresses at (i) subsidence deformation from the NW–SE and (ii) Alpine deformation from N–S increased the overall fracture aperture and permeability. In each case, increasing permeability is associated with open fractures parallel to the orientation of the loading stages and with fracture densities. The anisotropy of permeability is increased by the density and connectedness of the fracture network and affected by shear dilation. The two far-field stresses simultaneously acting within the selected fracture substructure at a different magnitude and orientation do not necessarily cancel each other out in the mechanical deformation modelling. These stresses affect the overall aperture and permeability distributions and the flow patterns. These effects – potentially ignored in simpler stress-dependent permeability – can result in significant inaccuracies in permeability estimation.

A Weak Galerkin Mixed Finite Element Method for Linear Elasticity Without Enforced Symmetry

A Weak Galerkin Mixed Finite Element Method for Linear Elasticity Without Enforced Symmetry

Analysis of a $$\varvec{P}_1\oplus \varvec{RT}_0$$ finite element method for linear elasticity with Dirichlet and mixed boundary conditions

Analysis of a $$\varvec{P}_1\oplus \varvec{RT}_0$$ finite element method for linear elasticity with Dirichlet and mixed boundary conditions

Comparing linear damage hypothesis to linear elastic fracture mechanics in the estimation of fatigue life in a high speed light craft

Linear elastic fracture mechanics methods provide a more comprehensive representation of crack propagation compared to traditional methods such as the linear damage hypothesis (or SN curve approach). These techniques have been widely adopted in the aerospace industry, however, their usage in the design of marine structures remains limited. The presented research uses full-scale trial data measured onboard a 111 m wave-piercing catamaran to compare the results obtained from linear elastic fracture mechanics and SN curve-based methods. The results reveal significant differences in estimated fatigue life between SN curve-based methods and fracture mechanics methods. These differences are likely due to limitations in the fracture mechanics model during the crack initiation phase. Changes in fracture mechanics parameters also had a significant effect on fatigue life, suggesting that if accuracy is important then material specific parameters are required. Despite the limitations shown, linear elastic fracture mechanics methods have a higher level of tailor-ability when compared to SN curve based methods and could offer benefits in situations such as the tracking of known flaws or in the assessment of changes to vessel configuration, or usage profiles.

Pushover analysis in slab-on-piles bridge using reinforced concrete-filled spun piles

Slab-on-piles is a bridge structure consisting of a continuous pile as a pier, pile head, and slab. Generally, the spun pile is chosen as the pile pier because of the quick construction and low maintenance. However, due to the hollow section with prestressed concrete, without filler, it has weakness in the form of brittle failure under bending moment and shear. Some studies mention that the initial failure occurs due to an explosion in the inner surface of the hollow spun pile or on the surface of the hole. The implementation spun pile for the slab-on-piles bridges should consider that behavior. Therefore, some practical engineers usually use concrete-infill treatment, however, the performance improvement in the nonlinear behavior needs to be known. This study investigates the use of hollow spun piles filled with concrete and normal reinforcement for a slab-on-piles bridge structure. This type of spun pile will be referred to as a reinforced concrete-filled spun pile (RCFSP). The location of slab-on-piles bridge is assumed to be built in Aceh, Indonesia. The height of the RCFSP on the slab-on-piles bridge is 6 m relative to the ground surface. A preliminary design using the linear elastic method is conducted using the response modification factor of 3.5. The slab-on-piles bridge requires 25 RCFSP for each bridge segment. Based on the pushover analysis method, this structure could not reach a performance point. A redesign is conducted using a response modification factor of 1.5. The redesign result shows that the structure requires 60 RCFSP and a performance point is found at a displacement of 85 mm in the longitudinal direction and 81 mm in the transversal direction. This research concludes that a slab-on-piles bridge is not efficient to be designed with a high value of response modification factor even though using the concrete-infill treatment.

Spectral Analysis of a Mixed Method for Linear Elasticity

Spectral Analysis of a Mixed Method for Linear Elasticity

Dirichlet and Neumann boundary conditions for a lattice Boltzmann scheme for linear elastic solids on arbitrary domains

We propose novel, second-order accurate boundary formulations of Dirichlet and Neumann boundary conditions for arbitrary curved boundaries, within the scope of our recently introduced lattice Boltzmann method for linear elasticity. The proposed methodology systematically constructs and analyzes the boundary formulations on the basis of the asymptotic expansion technique; thus, it is expected to be of general applicability to boundary conditions for lattice Boltzmann formulations, well beyond the focus of this paper. For Dirichlet boundary conditions, a modified version of the bounce-back method is developed, whereas the Neumann boundary conditions are based on a novel generalized ansatz proposed in this work. The Neumann boundary formulation requires information from one additional neighbor node, for which a finite difference algorithm is introduced that enables the handling of very general boundary geometries. The theoretical derivations are verified by convergence studies using manufactured solutions, as well as by comparison with the analytical solution of the classical plate with hole problem.

Reinforcement determination for anchorage zones of post-tensioned concrete beams

In post-tensioned concrete beams, the high concentrated compressive forces are transmitted to the concrete zones at the beam ends through the anchorage devices. As a result, they can burst and split if the concrete is not adequately reinforced. The paper determines the reinforcement in anchorage zones with axially loaded post-tensioned tendons using the linear elastic analysis method, which involves computing the state of stresses as linearly elastic, and the equilibrium-based plasticity approach method as strut-and-tie models to provide prestressing force paths as a truss structure. Some numerical models are also analyzed to clarify the present methods.

INFLUENCE OF COMPOSITE REINFORCEMENT ON THE DELOCALIZATION OF PLASTIC HINGES

Following multiple earthquakes in Algeria, large numbers of reinforced concrete structures have been severely damaged or destroyed, making it necessary to evaluate the actual seismic behavior of existing buildings. Classic linear elastic methods do not accurately represent the actual behavior of the structure, which makes it necessary to use calculation methods that take into account the post-elastic domain of the structure. The Push over method is a procedure that correctly predicts dynamic behavior in the event of a future earthquake. For frame structures, the formation of plastic hinges in the columns results in the transformation of the structure into a mechanism. This explains the need to give the post a higher strength than the beams.

A high order unfitted hybridizable discontinuous Galerkin method for linear elasticity

Abstract This work analyses a high-order hybridizable discontinuous Galerkin (HDG) method for the linear elasticity problem in a domain not necessarily polyhedral. The domain is approximated by a polyhedral computational domain where the HDG solution can be computed. The introduction of the rotation as one of the unknowns allows us to use the gradient of the displacements to obtain an explicit representation of the boundary data in the computational domain. The boundary data is transferred from the true boundary to the computational boundary by line integrals, where the integrand depends on the Cauchy stress tensor and the rotation. Under closeness assumptions between the computational and true boundaries, the scheme is shown to be well-posed and optimal error estimates are provided even in the nearly incompressible case. Numerical experiments in two dimensions are presented.

Effect of plasticity of the cladding with different thicknesses on the bearing capacity of the brittle base wall of RPV under PTS loads

In the research field of reactor pressure vessel (RPV) subjected to pressurized thermal shock (PTS), the traditional linear elastic analytical method generally ignores the plastic properties of cladding. In fact, the neutron irradiation in RPV is easy to cause the embrittlement of the base material rather than cladding. So the elastic-plastic parameters of cladding are introduced into the FE model of the RPV with a sub-clad crack. The stress distributions in the thermal-mechanical coupling fields related to the base wall and cladding of different thicknesses are then obtained. The XFEM is used to simulate the crack growth in the nozzle area. The allowable internal pressure in the dangerous moment of the PTS is calculated to show the ultimate bearing capacity of the structure. The numerical results are compared with those only considering the elasticity of cladding. Furthermore, the law of the effect of plasticity of cladding on the structural safety is summarized.

A locking-free stabilized embedded discontinuous Galerkin method for linear elasticity with strong symmetric stress and continuous displacement trace approximation

A locking-free stabilized embedded discontinuous Galerkin method for linear elasticity with strong symmetric stress and continuous displacement trace approximation

A lowest-order locking-free nonconforming virtual element method based on the reduced integration technique for linear elasticity problems

We develop a lowest-order nonconforming virtual element method for planar linear elasticity, which can be viewed as an extension of the idea in Falk (1991) to the virtual element method (VEM), with the family of polygonal meshes satisfying a very general geometric assumption. The method is shown to be uniformly convergent for the nearly incompressible case with optimal rates of convergence. The crucial step is to establish the discrete Korn's inequality, yielding the coercivity of the discrete bilinear form. We also provide a unified locking-free scheme both for the conforming and nonconforming VEMs in the lowest-order case. Numerical results validate the feasibility and effectiveness of the proposed numerical algorithms.

Mortaring for linear elasticity using mixed and stabilized finite elements

The purpose of this work is to study mortar methods for linear elasticity using standard low order finite element spaces. Based on residual stabilization, we introduce a stabilized mortar method for linear elasticity and compare it to the unstabilized mixed mortar method. For simplicity, both methods use a Lagrange multiplier defined on a trace mesh inherited from one side of the interface only. We derive a quasi-optimality estimate for the stabilized method and present the stability criteria of the mixed P1−P1 approximation. Our numerical results demonstrate the stability and the convergence of the methods for tie contact problems. Moreover, the results show that the mixed method can be successfully extended to three dimensional problems.

A locking-free staggered DG method for the Biot system of poroelasticity on general polygonal meshes

AbstractIn this paper we propose and analyze a staggered discontinuous Galerkin method for a five-field formulation of the Biot system of poroelasticity on general polygonal meshes. Elasticity is equipped with a stress–displacement–rotation formulation with weak stress symmetry for arbitrary polynomial orders, which extends the piecewise constant approximation developed in Zhao and Park (2020, A staggered cell-centered DG method for linear elasticity on polygonal meshes, SIAM J. Sci. Comput.42, A2158–A2181). The proposed method is locking-free and can handle highly distorted grids, possibly including hanging nodes, which is desirable for practical applications. We prove the convergence estimates for the semidiscrete scheme and fully discrete scheme for all the variables in their natural norms. In particular, the stability and convergence analyses do not need a uniformly positive storativity coefficient. Moreover, to reduce the size of the global system, we propose a five-field-formulation-based fixed stress splitting scheme, where the linear convergence of the scheme is proved. Several numerical experiments are carried out to confirm the optimal convergence rates and the locking-free property of the proposed method.

Equivalent linearization method for seismic analysis and design of self-centering structures

Although seismic response of engineering structures can be obtained through dynamic nonlinear analysis, approximate linear elastic analysis method is often adopted to reduce the computational effort and simplify the design procedure. Due to the excellent seismic performance, self-centering (SC) concrete structures are receiving more and more attention, but there is no such an equivalent linearization method especially suitable for SC concrete structures. In this study, the influence of hysteretic behavior on maximum inelastic displacement is described conceptually, and the estimation accuracy of four classic equivalent linearization methods are explored for SC models, the results show that the absolute mean displacement errors from classic methods mostly appear in the range of 20% to 30%, and most of the mean displacement errors is negative, which is unsafe for the performance-based seismic analysis and design. Then, an empirical equivalent linearization method is proposed for SC systems by a series of dynamic nonlinear analysis and regression analysis, it is found that the estimation accuracy of the proposed method is better than classic methods, and the standard deviation of the proposed method is basically at the same level as that of the classic methods. Finally, the proposed method is applied to the displacement-based design approach, the nonlinear analysis shows that the design targets can be well meet, and the designed SC concrete structure shows superior self-centering and energy dissipation capacity.