Study and application of physics-based deformable curves and surfaces

The finite element method is applied to generate primitives that build continuous deformable shapes designed to support a new free-form modeling paradigm. The primitives autonomously deform to minimize an energy functional subject to user controlled geometric constraints and loads. The approach requires less user input than conventional free-form modeling approaches because the shape can be parameterized independently of the number of degrees of freedom needed to describe the shape.Both a curve and a surface finite element are developed. The properties of these geometric primitives have been engineered to support an interactive three phase approach for defining very fair free-form shapes as found in automobiles, ship hulls and car bodies. The shape's character lines or folds and edges are defined with deformable curve segments. These character lines are then "skinned" with a deformable surface. The final shape is sculpted interactively by applying loads to the surface to control the surface shape between character lines. Shapes created with this technique enjoy the advantage that they are already meshed for further finite element analysis.

This paper presents an efficient inverse analysis technique for the identification of an unknown boundary condition in a finite element method (FEM) on a small memory capacity machine such as a personal computer. The author has previously presented the FEM of inverse analysis introducing an inverse compliance matrix that uses an influence function into the stiffness matrix for the unknown boundary. Since the stiffness matrix of the FEM becomes singular, following two calculation processes are adopted: (1) a calculation process which obtains an approximate solution by decreasing the effect of the inverse compliance in the stiffness, and (2) an iterative calculation process computing a correct solution from the approximation using (1). First, a penalty function method is used to decrease the rank of a singular stiffness matrix in (1). Then, the number for computing LDU decomposed matrix becomes twice in comparison with fourth times in the previous paper. Next, an efficient calculation method is presented using an attack technique based on both accelerative moving lower and upper bounds in (2). Moreover, a zooming identification method is developed, owing to an improvement of node displacements on and near the edges. Therefore, this technique makes it possible to establish an efficient inverse analysis for the identification of the unknown boundary. Finally, the validity of the inverse analysis technique is confirmed from the numerical solution of a three-dimensional inverse finite element analysis model, as an example of an elastic structure with reinforced members under tension, carried out on a small memory capacity machine.

This paper focus on the treating the multi freedom constraints in geometrically nonlinear buckling and post buckling analysis of truss structure using finite element method. The solution of geometrically nonlinear buckling problem of truss structure having multi freedom constraints is required to incorporate the boundary constraints to the nonlinear master stiffness equation. This work proposes approach to impose the multi freedom constraints and construct stiffness equation for solving the nonlinear buckling problems of truss structures using Penalty function method. The nonlinear balanced equations for buckling analysis of truss structures are developed by minimization of the augmented potential energy function of system by incorporating the multi freedom constraints and changing the constrained problem to the non-constrained problem using Penalty objective function. Using the arc length method, this research proposes the incremental-iterative algorithm for solving the nonlinear balanced equations. Based on proposed algorithm, the calculation program for determining equilibrium paths is written. The numerical test results show the efficiency of proposed method in analysing buckling and post buckling behaviour of truss structures.

Based on the shield tunnel engineering in weathered granite stratum in Xiamen, Stochastic calculations, by combining the random field theory and the finite difference analysis together with Monte Carlo simulation, are used to carry out the change law of the characteristics of surface deformation curve and surface deformation model. Results show that with the increase of the vertical scales of fluctuation, the decrease of the transverse scales of fluctuation or the increase of the coefficient of variation, the low peak distribution characteristics of the location of the maximum surface settlement induced by shield tunneling become more obvious, and the randomness and chaos of the shape of surface deformation curve gradually increase. The diversity of surface deformation model is affected by parameter correlation and randomness. Under the condition of small transverse scales of fluctuation and large vertical scales of fluctuation, the sensitivity of coefficient of variation to surface deformation mode is limited.

In this paper, we propose an effective finite element method (FEM) on the basis of domain decomposition method. In the domain decomposition method, the domain of structure is decomposed into subdomains, which are connected each other with an independent interface using a penalty function method. Using this FEM, the analysis of the whole structure can be carried out by analyzing the individual subdomain. As a numerical example, the stress analysis of an aircraft structural panel repaired with bonded composite patches is made, and the efficiency and the accuracy of the FEM are verified. The FEM is also used to carry out several parametric studies to examine the effects of patch shape and size on the stress fields in the repaired structural panel and composite patches. Finally, we determine the optimum shape and size of a composite patch to endure the maximum tensile applied stress by a mathematical programming.

In some simulations like virtual surgery, an accurate surface deformation method is needed. Many deformation methods focus on the whole model swing and twist. Few methods focus on surface deformation. For the surface deformation method, two necessary characteristics are needed: the accuracy and real-time performance. Some traditional methods, such as position-based dynamics (PBD) and mass-spring method (MSM), focus more on the real-time performance. Others like the finite element method (FEM) focus more on the accuracy. To balance these two characteristics, we propose a hybrid mesh deformation method for accurate surface deformation based on FEM and PBD. Firstly, we construct a hybrid mesh, which is composed of a coarse volume mesh and a fine surface mesh. Secondly, we implement FEM on coarse volume mesh and PBD on fine surface mesh, and the deformation of fine surface mesh is constrained by the displacement of the coarse volume mesh. Thirdly, we introduced a small incision process for our proposed method. Finally, we implemented our method on a simple deformation simulation and a small incision simulation. The result shows an accurate surface deformation performance by implementing our method. The incision effect shows the compatibility of our proposed method. In conclusion, our proposed method acquires a better trade-off between accuracy and real-time performance.

In order to employ the classical Rayleigh-Rite and the popular finite element methods to model different structural regions so that each is used to its fullest advantage, a coupled Rayleigh-Rite and finite element formulation using the penalty function method is presented. The formulation is based on a constrained variational principle. Along the interface of two different regions, deformations obtained from the Rayleigh-Ritz method are set equal to deformations obtained from the finite element method. The potential energy of the Rayleigh-Rite and finite element regions with these deformation constraints is used to derive a coupled stiffness matrix. This coupled stiffness matrix contains stiffness contributions from each region and an interface stiffness contribution from the constraints. The derivation is given for one dimensional coupling of a beam and two dimensional coupling of an equivalent plate with membrane finite elements to model a wing-like structure with box beam and leadingltrailing edges. Displacements and stresses using the coupled analysis are compared with those of using a single finite element analysis. Results indicate that using the coupled RayleighRite and finite element analysis produces results with a level of accuracy approaching that of a finite element analysis, while providing enhanced modeling flexibility.

Introduction. An important factor determining the effectiveness of protective structures in urban construction projects is the ability of their enclosing elements to maintain their protective functions under combat conditions, block the impact of damaging factors caused by air, missile, and artillery strikes, and protect people from debris and fragments of building structures. A pressing issue today, in the context of a full-scale invasion by an aggressor country, is the protection of critical infrastructure, particularly energy facilities and energy communications. To provide such protection, specially equipped protective structures are used, primarily constructed from reinforced concrete monolithic enclosing elements. Research Objective. To justify a general computational and theoretical approach to methods for calculating the protective capacity of modular shelters in accordance with the standards in force in Ukraine, specifically DBN V.2.2-5:2023 “Civil Defence Structures. Buildings and Structures,” under the impact of an explosive shock wave. Research Methods. The analysis of structural destruction was performed with consideration of relevant plasticity and strength theories. Modern computational technologies, utilizing advanced software and numerical algorithms, were employed for the calculations. Computational procedures were based on the explicit integration method for dynamic equations over time, the finite element method, and the description of contact interactions using the penalty function method. Mathematical models of materials under high-speed deformation were applied, accounting for their nonlinear properties and failure criteria in accordance with the relevant strength theories. Research Results. Patterns of correlation between explosion parameters and the stability of structural elements, in particular walls made of concrete lightweight blocks, have been established, which is important for assessing their residual protective capacity. The use of modern numerical modeling methods—including the finite element method, explicit integration of dynamic equations, contact interaction models, and nonlinear material models—enabled insight into the mechanisms of destruction and indicators of loss of integrity of protective structures as a result of explosions. This analysis included the most critical combination of explosion parameters, with a TNT equivalent charge of m (TNT) = 718.2 kg. The mechanisms of destruction or integrity loss in shelter structures were investigated, and their relationship to the performance of protective functions under an explosion with a TNT equivalent charge of m (TNT) = 30 kg and a minimum distance from the epicenter to the shelter surface of L = 0.5 m. Distributions of plate deformations were obtained for blast wave pressure applied to the shelter structure from the side, the end (closer to the door), and above the upper horizontal surface in the middle.

Dynamic analysis of arbitrarily restrained stiffened plate under moving loads

This paper presents an inverse analysis method for the identification of unknown boundary condition in elastoplastic state, using a finite element method (FEM) on a small memory capacity machine such as a microcomputer and a personal computer. This inverse analysis method is composed of following two calculation processes: an identification process which obtains a solution in elastic state, and a direct analysis in elastoplastic state based on the identified results from. For efficient identification, uses a penalty function method and an attack technique based on both accelerative moving lower and upper bounds. A zooming identification method is available for improvement of the identification accuracy. adopts a triple-tandem-type substructuring method as an efficient calculation method. Therefore, we establish an efficient inverse analysis method for the identification of unknown boundary condition in elastoplastic state. Finally, the validity of the inverse analysis method is confirmed from the numerical solution of a three-dimensional finite element model, as an example of V-shaped grooved structure with reinforced members under tension, executed on a small machine.

A numerical approach is described for the analysis of scattering from dielectric obstacles in a rectangular waveguide. The approach is a combination of the finite-element method and the analytical solution. In order to save computer memory, the substructure method is introduced in the finite-element method. To combine the uniform waveguide region with the finite-element-method region, evanescent modes and propagating modes are considered in the analytical solution. Spurious fields like the spurious solutions generated in the finite-element analysis of three-dimensional eigenvalue problems can appear in the three-dimensional discontinuity problems when the variational expression in terms of three components of the magnetic field is used. To suppress and eliminate the spurious fields, the penalty function method is also introduced. To confirm the validity and usefulness of the approach, numerical examples are shown for a rectangular dielectric scattering obstacle in a waveguide.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Delineating regions of interest (ROIs) on each phase of four-dimensional (4D) computed tomography (CT) images is an essential step for 4D radiotherapy. The requirement of manual phase-by-phase contouring prohibits the routine use of 4D radiotherapy. This paper develops an automatic re-contouring algorithm that combines techniques of deformable registration and surface construction. ROIs are manually contoured slice-by-slice in the reference phase image. A reference surface is constructed based on these reference contours using a triangulated surface construction technique. The deformable registration technique provides the voxel-to-voxel mapping between the reference phase and the test phase. The vertices of the reference surface are displaced in accordance with the deformation map, resulting in a deformed surface. The new contours are reconstructed by cutting the deformed surface slice-by-slice along the transversal, sagittal or coronal direction. Since both the inputs and outputs of our automatic re-contouring algorithm are contours, it is relatively easy to cope with any treatment planning system. We tested our automatic re-contouring algorithm using a deformable phantom and 4D CT images of six lung cancer patients. The proposed algorithm is validated by visual inspections and quantitative comparisons of the automatic re-contours with both the gold standard segmentations and the manual contours. Based on the automatic delineated ROIs, changes of tumour and sensitive structures during respiration are quantitatively analysed. This algorithm could also be used to re-contour daily images for treatment evaluation and adaptive radiotherapy.

Discrete element method (DEM) was employed to model the particle-particle and particle-screen interactions. Spherical and non-spherical particles were also modelled to gain a more accurate simulation of screening. A virtual screening model and a three-dimensional geometry of a vibrating screen were set up to perform a simulation of screening process using DEM and a finite element analysis, respectively. DEM and finite element method (FEM) were coupled to present a simulation of the interactions between particles and screen surface in a virtual screening process. After launched this coupling, stress on the screen surface and deformation of screen surface were obtained. It turns out that this coupling method is feasible to predict stress distributions and deformation of screen surface, meanwhile, this method also provides a reference to those engineering problems which are hard to be analysed and solved with only FEM or DEM.

In order to analyze deformation and stress state of round link chain which it is generated by instant impact for sudden loading between the chains during the working condition, the method of symmetric penalty function was adopted to analyze contact between round link chains; and the finite element software ANSYS LS-DYNA was further used to carry on nonlinear contact analysis, the displacement curves , the stress and deformation with time were gained during the process of impact by simulating the process of the instant impact of chains. The results show that it is circular to the contact area of round link chains and it is the main reasons of damage that the greater stress and deformation of impact is caused when time lasts 0.05s through theoretical analysis and finite element analysis software. The theory equations of load conditions and the method of finite elements can provide a theoretical basis and simulation methods for analyzing the round link chain driving in a variety of different working conditions under the conditions of impact.

Finite-element analysis of an overturned fold using a viscous-fluid model