Finite Element Basis Research Articles

Fatigue life assessment of welded joints under sequences of bending and torsion loading blocks of different lengths

AbstractIn this work, the nominal stress concept, the notch stress approach and two critical plane approaches are used to analyse the fatigue endurance of a pipe‐to‐plate welded joint subjected to complex loading histories. Both the pipe and the plate were made of S355JR steel. Starting from already known fatigue endurance curves obtained for the same specimens under pure bending and pure torsion, a first series of tests was conducted, in which specimens were loaded in bending for a given fraction of the estimated life and then in torsion until failure. A similar series of tests was then carried out by changing the loading order: specimens were firstly loaded in torsion for a given fraction of the estimated endurance and then in bending until failure. The whole test campaign was repeated for two different fractions of the estimated life, that is, 0.3 and 0.45, respectively. After that, additional three series of tests were carried out, in which the specimens were subjected to consecutive sequences of bending and torsion blocks of different lengths (short, medium and long, respectively); the relative length of the bending and torsion block in each series was determined in order to produce the same damage. The experimental results, in terms of total damage at failure, were analysed using the Palmgren–Miner hypothesis. For all the assessment methods, the characteristic endurance curves were firstly calibrated on the basis of finite element (FE) analyses and of the experimental results obtained under pure bending and pure torsion loadings. The observed damage at failure resulted always greater than 0.5 for all the employed methods and greater than 1 for most of the tests. The different methods gave similar results, with the critical plane methods giving a slightly more stable damage at failure and a correct determination of the failure location. For all the methods, the damage at failure slightly reduces as the block length shortens.

Discontinuous finite volume element method for a coupled Navier-Stokes-Cahn-Hilliard phase field model

In this paper, we propose a discontinuous finite volume element method to solve a phase field model for two immiscible incompressible fluids. In this finite volume element scheme, discontinuous linear finite element basis functions are used to approximate the velocity, phase function, and chemical potential while piecewise constants are used to approximate the pressure. This numerical method is efficient, optimally convergent, conserving the mass, convenient to implement, flexible for mesh refinement, and easy to handle complex geometries with different types of boundary conditions. We rigorously prove the mass conservation property and the discrete energy dissipation for the proposed fully discrete discontinuous finite volume element scheme. Using numerical tests, we verify the accuracy, confirm the mass conservation and the energy law, test the influence of surface tension and small density variations, and simulate the driven cavity, the Rayleigh-Taylor instability.

A linearity preserving nodal variation limiting algorithm for continuous Galerkin discretization of ideal MHD equations

In this work, a stabilized continuous Galerkin (CG) method for magnetohydrodynamics (MHD) is presented. Ideal, compressible inviscid MHD equations are discretized in space on unstructured meshes using piecewise linear or bilinear finite element bases to get a semi-discrete scheme. Stabilization is then introduced to the semi-discrete method in a strategy that follows the algebraic flux correction paradigm. This involves adding some artificial diffusion to the high order, semi-discrete method and mass lumping in the time derivative term. The result is a low order method that provides local extremum diminishing properties for hyperbolic systems. The difference between the low order method and the high order method is scaled element-wise using a limiter and added to the low order scheme. The limiter is solution dependent and computed via an iterative linearity preserving nodal variation limiting strategy. The stabilization also involves an optional consistent background high order dissipation that reduces phase errors. The resulting stabilized scheme is a semi-discrete method that can be applied to inviscid shock MHD problems and may be even extended to resistive and viscous MHD problems. To satisfy the divergence free constraint of the MHD equations, we add parabolic divergence cleaning to the system. Various time integration methods can be used to discretize the scheme in time. We demonstrate the robustness of the scheme by solving several shock MHD problems.

Second-generation wavelet finite element based on the lifting scheme for GPR simulation

Ground-penetrating radar (GPR) is a highly efficient, fast and non-destructive exploration method for shallow surfaces. High-precision numerical simulation method is employed to improve the interpretation precision of detection. Second-generation wavelet finite element is introduced into the forward modeling of the GPR. As the finite element basis function, the second-generation wavelet scaling function constructed by the scheme is characterized as having multiple scales and resolutions. The function can change the analytical scale arbitrarily according to actual needs. We can adopt a small analysis scale at a large gradient to improve the precision of analysis while adopting a large analytical scale at a small gradient to improve the efficiency of analysis. This approach is beneficial to capture the local mutation characteristics of the solution and improve the resolution without changing mesh subdivision to realize the efficient solution of the forward GPR problem. The algorithm is applied to the numerical simulation of line current radiation source and tunnel non-dense lining model with analytical solutions. Result show that the solution results of the second-generation wavelet finite element are in agreement with the analytical solutions and the conventional finite element solutions, thereby verifying the accuracy of the second-generation wavelet finite element algorithm. Furthermore, the second-generation wavelet finite element algorithm can change the analysis scale arbitrarily according to the actual problem without subdividing grids again. The adaptive algorithm is superior to traditional scheme in grid refinement and basis function order increase, which makes this algorithm suitable for solving complex GPR forward-modeling problems with large gradient and singularity.

An adaptive composite discontinuous Galerkin method for elliptic problems on complicated domains with discontinuous coefficients

In this paper, we introduce the multi-region discontinuous Galerkin composite finite element method (MRDGCFEM) with hp-adaptivity for the discretization of second-order elliptic partial differential equations with discontinuous coefficients. This method allows for the approximation of problems posed on computational domains where the jumps in the diffusion coefficient form a micro-structure. Standard numerical methods could be used for such problems but the computational effort may be extremely high. Small enough elements to represent the underlying pattern in the diffusion coefficient have to be used. In contrast, the dimension of the underlying MRDGCFE space is independent of the complexity of the diffusion coefficient pattern. The key idea is that the jumps in the diffusion coefficient are no longer resolved by the mesh where the problem is solved; instead, the finite element basis (or shape) functions are adapted to the diffusion pattern allowing for much coarser meshes. In this paper, we employ hp-adaptivity on a series of test cases highlighting the practical application of the proposed numerical scheme.

Finite element (GFEM) simulations on the effect of microwave heating for lossy dielectric samples with various shapes (circle, square and triangle)

Purpose This paper aims to investigate the thermal performance involving larger heating rate, targeted heating, heating with least non-uniformity of the spatial distribution of temperature and larger penetration of heating within samples vs shapes of samples (circle, square and triangular). Design/methodology/approach Galerkin finite element method (GFEM) with adaptive meshing in a composite domain (free space and sample) is used in an in-house computer code. The finite element meshing is done in a composite domain involving triangle embedded within a semicircular hypothetical domain. The comparison of heating pattern is done for various shapes of samples involving identical cross-sectional area. Test cases reveal that triangular samples can induce larger penetration of heat and multiple heating fronts. A representative material (beef) with high dielectric loss corresponding to larger microwave power or heat absorption in contrast to low lossy samples is considered for the current study. The average power absorption within lossy samples has been computed using the spatial distribution and finite element basis sets. Four regimes have been selected based on various local maxima of the average power for detailed investigation. These regimes are selected based on thin, thick and intermediate limits of the sample size corresponding to the constant area of cross section, Ac involving circle or square or triangle. Findings The thin sample limit (Regime 1) corresponds to samples with spatially invariant power absorption, whereas power absorption attenuates from exposed to unexposed faces for thick samples (Regime 4). In Regimes 2 and 3, the average power absorption non-monotonically varies with sample size or area of cross section (Ac) and a few maxima of average power occur for fixed values of Ac involving various shapes. The spatial characteristics of power and temperature have been critically analyzed for all cross sections at each regime for lossy samples. Triangular samples are found to exhibit occurrence of multiple heating fronts for large samples (Regimes 3 and 4). Practical implications Length scales of samples of various shapes (circle, square and triangle) can be represented via Regimes 1-4. Regime 1 exhibits the identical heating rate for lateral and radial irradiations for any shapes of lossy samples. Regime 2 depicts that a larger heating rate with larger temperature non-uniformity can occur for square and triangular-Type 1 lossy sample during lateral irradiation. Regime 3 depicts that the penetration of heat at the core is larger for triangular samples compared to circle or square samples for lateral or radial irradiation. Regime 4 depicts that the penetration of heat is still larger for triangular samples compared to circular or square samples. Regimes 3 and 4 depict the occurrence of multiple heating fronts in triangular samples. In general, current analysis recommends the triangular samples which is also associated with larger values of temperature variation within samples. Originality/value GFEM with generalized mesh generation for all geometries has been implemented. The dielectric samples of any shape are surrounded by the circular shaped air medium. The unified mesh generation within the sample connected with circular air medium has been demonstrated. The algorithm also demonstrates the implementation of various complex boundary conditions in residuals. The numerical results compare the heating patterns for all geometries involving identical areas. The thermal characteristics are shown with a few generalized trends on enhanced heating or targeted heating. The circle or square or triangle (Type 1 or Type 2) can be selected based on specific heating objectives for length scales within various regimes.

Biomechanical effects of corticotomy facilitated orthodontic anterior retraction: a 3-dimensional finite element analysis

The objective of this study was to assess the biomechanical effects of different corticotomy designs used for orthodontic anterior retraction through finite element analysis. Materials and methods: A basic finite element model simulating retraction of anterior teeth was built reversely from CBCT films of an adult patient with protruded maxillary anterior teeth. Another thirteen FE models were created according to different corticotomy designs varied with site width and the extent of incision. The initial displacement, Von Mises stress and pressure stress of dento-alveolar structures was computerized and analyzed. Results: Corticotomy can increase the initial displacement of anterior segment including teeth and surrounding alveolar bone, change the distribution of Von Mises stress in cancellous bone and the pressure stress in periodontal ligament of anterior teeth. When the incision was near the periphery of apical, the anterior segment showed the greatest displacement, the cancellous bone at either sockets or incision region showed the maximum stress. Bilateral incision combined with palatal incision showed approximate initial displacement and stress distribution with circumscribing incision. While the incision width increased, the biomechanical effects of corticotomy amplified. Conclusions: Varied corticotomy designs can change the biomechanical effects on dento-alveolar structures. The incision near the periphery of apical and bilateral incision combined with palatal incision may be the optimized design used for retraction of anterior teeth.

Discrete hydrodynamics near solid walls: Non-Markovian effects and the slip boundary condition.

A simple Markovian theory for the prediction of averages and correlations of discrete hydrodynamics near parallel solid walls is presented. The discrete momentum of bins is defined through a finite element basis function. The effect of the walls on the fluid is through irreversible extended friction forces appearing in the very equations of hydrodynamics. The Markovian assumption is critically assessed from the exponential decay of the eigenvalues of the correlation matrix of the discrete transverse momentum. We observe that for bins smaller than molecular dimensions, allowing one to resolve the density layering near the wall, the dynamics near the wall is non-Markovian. Bins larger than the molecular size do behave in a Markovian way. We measure the nonlocal viscosity and frictions kernels that appear in the discrete hydrodynamic equations, which are given in terms of Green-Kubo formulas. They suffer dramatically from the plateau problem. We use a recent procedure for reliably extracting the transport kernels out of the plateau-problematic Green-Kubo formula. With the so-measured transport kernels the nonlocal theory predicts very well the decay of the average of the transverse momentum when the initial velocity profile is a plug flow. The theory allows us to derive the slip boundary condition with microscopic expressions for the slip length and the hydrodynamic position of the wall. The slip boundary condition is not satisfied at the initial stages of the discontinous plug flow, but good agreement is obtained at later stages.

Residual-Type APosterioriError Estimates for 3-D Low-Frequency Stable Maxwell Formulations in Both Frequency and Time Domains

In this article, residual-type a posteriori error estimates developed in our previous work for magnetostatic and eddy-current problems are extended to low-frequency (LF) Maxwell problems using A/φ formulation, where both inductive and capacitive effects can be handled simultaneously. Classical low-order finite-element basis (LOFEB) as well as high-order finite-element basis (HOFEB) of the edge and nodal types are adopted in numerical examples to evaluate the performance of the proposed estimators.

Discontinuous finite-element quadrature sets based on icosahedron for the discrete ordinates method

The discrete ordinates method (SN) is one of the major shielding calculation method, which is suitable for solving deep-penetration transport problems. Our objective is to explore the available quadrature sets and to improve the accuracy in shielding problems involving strong anisotropy. The linear discontinuous finite-element (LDFE) quadrature sets based on the icosahedron (in short, ICLDFE quadrature sets) are developed by defining projected points on the surfaces of the icosahedron. Weights are then introduced in the integration of the discontinuous finite-element basis functions in the relevant angular regions. The multivariate secant method is used to optimize the discrete directions and their corresponding weights. The numerical integration of polynomials in the direction cosines and the Kobayashi benchmark are used to analyze and verify the properties of these new quadrature sets. Results show that the ICLDFE quadrature sets can exactly integrate the zero-order and first-order of the spherical harmonic functions over one-twentieth of the spherical surface. As for the Kobayashi benchmark problem, the maximum relative error between the fifth-order ICLDFE quadrature sets and references is only −0.55%. The ICLDFE quadrature sets provide better integration precision of the spherical harmonic functions in local discrete angle domains and higher accuracy for simple shielding problems.

Numerical heat flow visualization analysis on enhanced thermal processing for various shapes of containers during thermal convection

PurposeThe purpose of this paper is to study thermal (natural) convection in nine different containers involving the same area (area= 1 sq. unit) and identical heat input at the bottom wall (isothermal/sinusoidal heating). Containers are categorized into three classes based on geometric configurations [Class 1 (square, tilted square and parallelogram), Class 2 (trapezoidal type 1, trapezoidal type 2 and triangle) and Class 3 (convex, concave and triangle with curved hypotenuse)].Design/methodology/approachThe governing equations are solved by using the Galerkin finite element method for various processing fluids (Pr= 0.025 and 155) and Rayleigh numbers (103 ≤ Ra≤ 105) involving nine different containers. Finite element-based heat flow visualization via heatlines has been adopted to study heat distribution at various sections. Average Nusselt number at the bottom wall (Nub¯) and spatially average temperature (θ^) have also been calculated based on finite element basis functions.FindingsBased on enhanced heating criteria (higherNub¯and higher θ^), the containers are preferred as follows, Class 1: square and parallelogram, Class 2: trapezoidal type 1 and trapezoidal type 2 and Class 3: convex (higher θ^) and concave (higherNub¯).Practical implicationsThe comparison of heat flow distributions and isotherms in nine containers gives a clear perspective for choosing appropriate containers at various process parameters (PrandRa). The results for current work may be useful to obtain enhancement of the thermal processing rate in various process industries.Originality/valueHeatlines provide a complete understanding of heat flow path and heat distribution within nine containers. Various cold zones and thermal mixing zones have been highlighted and these zones are found to be altered with various shapes of containers. The importance of containers with curved walls for enhanced thermal processing rate is clearly established.

Projective Geometry of Wachspress Coordinates

We show that there is a unique hypersurface of minimal degree passing through the non-faces of a polytope which is defined by a simple hyperplane arrangement. This generalizes the construction of the adjoint curve of a polygon by Wachspress (A rational finite element basis, Academic Press, New York, 1975). The defining polynomial of our adjoint hypersurface is the adjoint polynomial introduced by Warren (Adv Comput Math 6:97–108, 1996). This is a key ingredient for the definition of Wachspress coordinates, which are barycentric coordinates on an arbitrary convex polytope. The adjoint polynomial also appears both in algebraic statistics, when studying the moments of uniform probability distributions on polytopes, and in intersection theory, when computing Segre classes of monomial schemes. We describe the Wachspress map, the rational map defined by the Wachspress coordinates, and the Wachspress variety, the image of this map. The inverse of the Wachspress map is the projection from the linear span of the image of the adjoint hypersurface. To relate adjoints of polytopes to classical adjoints of divisors in algebraic geometry, we study irreducible hypersurfaces that have the same degree and multiplicity along the non-faces of a polytope as its defining hyperplane arrangement. We list all finitely many combinatorial types of polytopes in dimensions two and three for which such irreducible hypersurfaces exist. In the case of polygons, the general such curves are elliptic. In the three-dimensional case, the general such surfaces are either K3 or elliptic.

The Structural Behaviour of a Ship’s Sub-Block During Lifting Operation

The process of lifting a ship’s block is one of the important process in shipbuilding. The purpose of lifting or transfering of the blocks is to relocate the block to a new position before joining with other blocks. Prior to the lifting operation of ship’s sub-block, some stress and deflection analysis shall be done, in order to assess the magnitude of the deformation and the stresses acting on the structural members of the block. Based on the assessment, some changes in lifting operation can be intiated for example changing the lifting eye pad location to minimize plate deformation and bucking of structural members. In this study, the structural behaviour of a block was investigated using basic finite element method in order to simulate the deflections and stresses during the lifting operation. The initial dimension of the sub-block that was being investigated are with its dimensions: 21 meters in length, 16 meters in width, 4 meters in height. The type of material of all the structural components used in the sub-block is High Tensile Steel DH36. The investigation used Multiframe software. There are four case studies conducted with varying padeye location and number of lifting eye pads used in a single lifting. The sub block is approximately at 160 tonnes. These results were assessed with the DNV-GL acceptance criteria which can be found in DNV-GL Rules for finite element analysis. The highest yield ulitilization factor was found in case study 3 at 0.864, where it did not comply with the permissible coarse mesh yield utilization factor which is limited to 0.80. The lowest yield utilization factor was found in case study 2 at 0.278. Using the DNV-GL acceptance criteria it is concluded that case study 2 is the best configuration in lifting the sub-block.

Improving the modified XFEM for optimal high‐order approximation

SummaryThis paper investigates the accuracy of high‐order extended finite element methods (XFEMs) for the solution of discontinuous problems with both straight and curved weak discontinuities in two dimensions. The modified XFEM, a specific form of the stable generalised finite element method, is found to offer advantages in cost and complexity over other approaches, but suffers from suboptimal rates of convergence due to spurious higher‐order contributions to the approximation space. An improved modified XFEM is presented, with basis functions “corrected” by projecting out higher‐order contributions that cannot be represented by the standard finite element basis. The resulting corrections are independent of the equations being solved and need be pre‐computed only once for geometric elements of a given order. An accurate numerical integration scheme that correctly integrates functions with curved discontinuities is also presented. Optimal rates of convergence are then recovered for Poisson problems with both straight and quadratically curved discontinuities for approximations up to order p ≤ 4. These are the first truly optimal convergence results achieved using the XFEM for a curved weak discontinuity and are also the first optimally convergent results achieved using the modified XFEM for any problem with approximations of order p>1. Almost optimal rates of convergence are recovered for an elastic problem with a circular weak discontinuity for approximations up to order p ≤ 4.

The Structural Behaviour of a Ship‟s Sub-Block During Lifting Operation

The process of lifting a ship’s block is one of the important process in shipbuilding. The purpose of lifting or transfering of the blocks is to relocate the block to a new position before joining with other blocks. Prior to the lifting operation of ship’s sub-block, some stress and deflection analysis shall be done, in order to assess the magnitude of the deformation and the stresses acting on the structural members of the block. Based on the assessment, some changes in lifting operation can be intiated for example changing the lifting eye pad location to minimize plate deformation and bucking of structural members. In this study, the structural behaviour of a block was investigated using basic finite element method in order to simulate the deflections and stresses during the lifting operation. The initial dimension of the sub-block that was being investigated are with its dimensions: 21 meters in length, 16 meters in width, 4 meters in height. The type of material of all the structural components used in the sub-block is High Tensile Steel DH36. The investigation used Multiframe software. There are four case studies conducted with varying padeye location and number of lifting eye pads used in a single lifting. The sub block is approximately at 160 tonnes. These results were assessed with the DNV-GL acceptance criteria which can be found in DNV-GL Rules for finite element analysis. The highest yield ulitilization factor was found in case study 3 at 0.864, where it did not comply with the permissible coarse mesh yield utilization factor which is limited to 0.80. The lowest yield utilization factor was found in case study 2 at 0.278. Using the DNV-GL acceptance criteria it is concluded that case study 2 is the best configuration in lifting the sub-block.

Identifying a fractional order and a space source term in a time-fractional diffusion-wave equation simultaneously

This paper is devoted to identify simultaneously a fractional order and a space source term in a multi-dimensional time-fractional diffusion-wave equation by the final time measurement data. We prove the uniqueness and stability of the inverse problem. Then we use the Levenberg–Marquardt method to recover the fractional order and the space source term simultaneously, and propose a finite dimensional approximation algorithm based on the linear finite element basis to find a regularized solution. Numerical examples in one-dimensional and two-dimensional cases are provided to illustrate the efficiency of the proposed algorithm.

Exact exchange-correlation potentials from ground-state electron densities

The quest for accurate exchange-correlation functionals has long remained a grand challenge in density functional theory (DFT), as it describes the many-electron quantum mechanical behavior through a computationally tractable quantity—the electron density—without resorting to multi-electron wave functions. The inverse DFT problem of mapping the ground-state density to its exchange-correlation potential is instrumental in aiding functional development in DFT. However, the lack of an accurate and systematically convergent approach has left the problem unresolved, heretofore. This work presents a numerically robust and accurate scheme to evaluate the exact exchange-correlation potentials from correlated ab-initio densities. We cast the inverse DFT problem as a constrained optimization problem and employ a finite-element basis—a systematically convergent and complete basis—to discretize the problem. We demonstrate the accuracy and efficacy of our approach for both weakly and strongly correlated molecular systems, including up to 58 electrons, showing relevance to realistic polyatomic molecules.

Grounds for the decision to strengthen reinforced concrete structures after short-term impulse loads, using Alluriquin HPP as an example

Introduction. Floorings of the turbine hall and installation sites of the HPP (PSS) are one of the most important reinforced concrete structures, as during operation they are subjected to significant process duties, including those not provided for by the project. Thus, during the testing of crane equipment on the floor surface of the installation site of the Alluriquin HPP under construction, the cargo weighing 22 tons fell, under the influence of which the floor slab was punched, which required a comprehensive study of the condition of the reinforced concrete structure of the floor and the surrounding area of the failure of structures, as well as the development of measures to strengthen the damaged structure. Materials and Methods. Visual and instrumental studies of the stress and strain state (SSS) of the reinforced concrete structure of the turbine hall slab and surrounding structures were carried out with the use of optical devices (MPB-3 reading microscope), Schmidt hammer to determine the strength of concrete structures, as well as the “reinforcement load removal” method to determine the actual stresses in the reinforcement of structures. Results. The punching of the reinforced concrete floor of the installation site with vertical displacements of the edges of through cracks up to 12 mm, as well as the system of cracks formed during the fall of cargo was revealed. The actual stresses in the reinforcement are determined by the “reinforcement load removal” method. On the basis of finite element modeling the actual condition of structures during the period of cargo fall and after the removal of the load is obtained. On the basis of the analysis of results of field and design studies the schematic diagram of strengthening of structures by carbon composite materials is developed. Conclusions. The actual SSS of the reinforced concrete floor of the installation site and its support structures during the period of the cargo fall and after the termination of the impulse load is established. The vertical displacement of the edges of the crack of the floor punching was 17.5 mm during the period of the fall of the load and 12 mm after the removal of the impulse load. Crack opening width in reinforced concrete structures in the cargo drop area reached 2 mm. At the moment when the cargo fell on the floor slab, the values of stresses in the reinforcement cage reached 200 MPa; after the impact — 76.2 MPa. With a view of the subsequent safe operation of the reinforced concrete floor and surrounding structures the basic schemes of their strengthening by external reinforcement on the basis of carbon fiber have been developed, which have been proved by calculation.

M6 USING PRS SCORES TO CLARIFY NOSOLOGICAL STRUCTURE OF ADHD AND OVERLAPPING EMOTION-RELATED TRAIT MEASURES

In this work, a stabilized continuous Galerkin (CG) method for magnetohydrodynamics (MHD) is presented. Ideal, compressible inviscid MHD equations are discretized in space on unstructured meshes using piecewise linear or bilinear finite element bases to get a semi-discrete scheme. Stabilization is then introduced to the semi-discrete method in a strategy that follows the algebraic flux correction paradigm. This involves adding some artificial diffusion to the high order, semi-discrete method and mass lumping in the time derivative term. The result is a low order method that provides local extremum diminishing properties for hyperbolic systems. The difference between the low order method and the high order method is scaled element-wise using a limiter and added to the low order scheme. The limiter is solution dependent and computed via an iterative linearity preserving nodal variation limiting strategy. The stabilization also involves an optional consistent background high order dissipation that reduces phase errors. The resulting stabilized scheme is a semi-discrete method that can be applied to inviscid shock MHD problems and may be even extended to resistive and viscous MHD problems. To satisfy the divergence free constraint of the MHD equations, we add parabolic divergence cleaning to the system. Various time integration methods can be used to discretize the scheme in time. We demonstrate the robustness of the scheme by solving several shock MHD problems.

A high-order multiscale finite-element method for time-domain elastic wave modeling in strongly heterogeneous media

Efficient and accurate numerical methods for elastic wave modeling in complex media have many important applications. However, it is fairly challenging to model elastic wave propagation in strongly heterogeneous media with high computational efficiency and high-order accuracy simultaneously. We develop a novel high-order multiscale finite-element method to model elastic wave propagation in strongly heterogeneous media in the time domain. The most important feature of our method is a generalization of standard multiscale finite element method by using high-order multiscale finite-element basis functions to capture the fine-scale heterogeneities on the coarse mesh, in contrast to conventional finite-element basis functions that are merely determined by the order of polynomials. These multiscale basis functions leads to a system matrix with significantly reduced dimension, thus enable us to solve the elastic wave equation on the coarse mesh with high-order accuracy and very low computational time cost. We use 2D and 3D numerical examples to demonstrate the superior efficiency and accuracy of our new modeling method compared with the conventional spectral-element method.