The Image-Based Finite Element Evaluation of the Deformed State

The article presents one of the possible approaches to modeling objects with anisotropic properties based on images of the study area. Data from such images are taken into account when building a numerical model. In this case, material inhomogeneity can be included by integrating the local stiffness matrix of each finite element with a certain weight function. The purpose of the presented work is to develop a finite element for the formation of a computational ensemble and simulation of mechanical behavior taking into account the data of two-dimensional medical images. To implement the proposed approach, we used the assumption that there is a correlation between the values in the image pixels and the elastic properties of the material. Meshing was based on a four-node plane finite element. This approach allows using the quantitative phase or scanning electronic images, as well as computed tomography data. A number of test problems for compression of elementary geometry samples were calculated. The distal part of the rat femur was considered as a model problem. A computed tomography scan of the sample was used to construct a numerical model taking into account the inhomogeneity of the material distribution inside the organ. The distribution field of the nodal displacements based on data obtained from the images of the study area is presented. Within the framework of a model problem, we considered how a computer tomograph resolution influences the quality of the obtained results. For this purpose, calculations were carried out based on compressed input medical images.

Prestress behaviour and ductility requirements in structures: solutions from a unified algebraic approach

This paper presents an algebraic approach that unifies both the elastic and limit theories of static structural analysis. This approach reveals several previously unpublished improvements, which are based on several dualities in the mathematical description. Firstly, we show a novel duality between the solutions to two different problems: the elastic solution to the internal forces of an externally loaded structure, and the nodal displacements induced by prestressing in one or several elements of the same structure. This duality is proven and discussed. The application of this solution to the limit state analysis is very productive, and includes the determination of the ductility requirements necessary to achieve full plastic behaviour, and the assessment of the prestress needed to limit or eliminate such requirements. The unified framework also allows to obtain the elasto-plastic deformed state at the beginning of the plastic structural collapse. We have also detailed the theoretical duality between two classes of structures—hyperstatic and hypostatic—which was derived from the linear algebra principles that define these solutions. Finally, we studied and exposed the dimensionality reduction of structural problems given by the singular value decomposition and the eigenvalues problem. An illustrative example that clearly illustrates all these points is provided.

Inhomogeneous Folding Modes in Infinite Lattices of Rigid Triangulated Miura-ori

Infinite two-dimensional tessellations of triangulated Miura-ori with rigid panels are known to exhibit only homogeneous modes of folding, thereby limiting their usefulness in engineering applications. In this work, we show that the corresponding one-dimensional lattices are less restricted and can exhibit inhomogeneous folding modes of deformation. We demonstrate this by looking at the modes in the null space of Bloch-reduced compatibility matrix in a nodal-displacement-based formulation, that is typically employed in the context of origami structural analysis. We compute the deformation modes that vary non-uniformly across the lattice depending on their wavelength, and identify the minimal number of modes that can represent such deformations. We then present a more efficient formulation based on folding-angles to study the deformation modes of infinite one-dimensional rigid triangulated origami lattices. We derive the degrees of freedom of the tessellations in terms of the minimal number of folding-angles that are required to capture the periodic inhomogeneous deformations of the infinite lattices. Within this formulation, we provide the framework to analytically derive the stiffness matrix of the lattice. Finally, we verify the new formulation by comparing the results with the bar-and-hinge model that is based on nodal-displacements. The observations from our work could have implications for the use of rigid panel origami lattices as acoustic metamaterials.

Static Behavior of a Retractable Suspen-Dome Structure

A new design of a radially retractable roof structure based on the concept of the suspen-dome is proposed in this paper. The radially foldable bar structure is strengthened by the lower cable-strut system to obtain a higher structural stiffness. Then the comparison of the static behavior between the retractable suspen-domes and their corresponding foldable bar shell with quadrangular mesh is discussed. Moreover, the effects of different structural and geometric parameters, such as the rise-to-span ratio, the cross-section area of beams, cables and struts, and the pre-stress level of the lower cable-strut system, on the nodal displacements and member forces are investigated systematically. The results show that higher structural stiffness is anticipated with the introduction of cable-strut systems into the hybrid structure. When the rise-to-span ratio is equal to 0.2, the maximal nodal displacement of the suspen-dome reaches the minimal value. The increase of the cross-section area of steel beams contributes an enormous amount to the structural stiffness. Increasing cable and strut sections has little impact on the mechanical behavior of suspen-domes. Moreover, the prestress level of cable-strut systems has a slight influence on the nodal displacements and member forces. Parametric analysis can be regarded as an essential basis for the optimization of the design of a retractable suspen-dome structure.

Finite element simulations of the effects of an extraoral device, RAMPA, on anterosuperior protraction of the maxilla and comparison with gHu-1 intraoral device

ABSTRACT Objectives To investigate the effects of an extraoral device, right-angle maxillary protraction appliance (RAMPA), combined with a semi-rapid maxillary expansion intraoral device (gHu-1) on the anterosuperior protraction of maxillary bone. Materials and Methods The finite element (FE) model included craniofacial bones and all sutures. The linear assumption was assumed for the FE simulations and the material properties of bones and sutures. The gHu-1 was simulated under screw activations equal to Δx = 0.25 and 0.5 mm in the lateral direction with and without RAMPA under a set of external forces {F1 = 2.94, F2 = 1.47, F3 = 4.44} N. Results Displacement contours, nodal displacements of 12 landmarks, and von Mises stresses were compared. Combining RAMPA and gHu-1 (with Δx = 0.25 mm) resulted in changes in the displacement of the front part of the maxilla near the mid-palatal suture from (0.02, −0.1, −0.02) mm to (0.02, 0.3, 0.8) mm. For gHu-1 with Δx = 0.5 mm, the displacement of the same part changed from (0.04, −0.04, −0.2) mm to (0.04, 0.3, 0) mm. Similar trends were found in other locations. Conclusions The findings are in agreement with the previous cephalometric clinical data of an 8-year-old patient and prove the positive effects of RAMPA on the anterosuperior protraction of the maxilla when it is combined with the intraoral device gHu-1. In addition, RAMPA does not interfere with the lateral expansion generated by the intraoral device.

Application of the Generalized Nonlinear Constitutive Law in 2D Shear Flexible Beam Structures

The paper presents a modified finite element method for nonlinear analysis of 2D beam structures. To take into account the influence of the shear flexibility, a Timoshenko beam element was adopted. The algorithm proposed enables using complex material laws without the need of implementing advanced constitutive models in finite element routines. The method is easy to implement in commonly available CAE software for linear analysis of beam structures. It allows to extend the functionality of these programs with material nonlinearities. By using the structure deformations, computed from the nodal displacements, and the presented here generalized nonlinear constitutive law, it is possible to iteratively reduce the bending, tensile and shear stiffnesses of the structures. By applying a beam model with a multi layered cross-section and generalized stresses and strains to obtain a representative constitutive law, it is easy to model not only the complex multi-material cross-sections, but also the advanced nonlinear constitutive laws (e.g. material softening in tension). The proposed method was implemented in the MATLAB environment, its performance was shown on the several numerical examples. The cross-sections such us a steel I-beam and a steel I-beam with a concrete encasement for different slenderness ratios were considered here. To verify the accuracy of the computations, all results are compared with the ones received from a commercial CAE software. The comparison reveals a good correlation between the reference model and the method proposed.

Large-Scale Truss-Sizing Optimization with Enhanced Hybrid HS Algorithm

Metaheuristic algorithms currently represent the standard approach to engineering optimization. A very challenging field is large-scale structural optimization, entailing hundreds of design variables and thousands of nonlinear constraints on element stresses and nodal displacements. However, very few studies documented the use of metaheuristic algorithms in large-scale structural optimization. In order to fill this gap, an enhanced hybrid harmony search (HS) algorithm for weight minimization of large-scale truss structures is presented in this study. The new algorithm, Large-Scale Structural Optimization–Hybrid Harmony Search JAYA (LSSO-HHSJA), developed here, combines a well-established method like HS with a very recent method like JAYA, which has the simplest and inherently most powerful search engine amongst metaheuristic optimizers. All stages of LSSO-HHSJA are aimed at reducing the number of structural analyses required in large-scale structural optimization. The basic idea is to move along descent directions to generate new trial designs, directly through the use of gradient information in the HS phase, indirectly by correcting trial designs with JA-based operators that push search towards the best design currently stored in the population or the best design included in a local neighborhood of the currently analyzed trial design. The proposed algorithm is tested in three large-scale weight minimization problems of truss structures. Optimization results obtained for the three benchmark examples, with up to 280 sizing variables and 37,374 nonlinear constraints, prove the efficiency of the proposed LSSO-HHSJA algorithm, which is very competitive with other HS and JAYA variants as well as with commercial gradient-based optimizers.

Formation of Moments Influence Matrix in Frame Based on Graph of its Design Scheme

A procedure is proposed for the automated construction of the bending moments influence matrix in the frame based on the graph of its discrete model. Forming the incidence matrix of the graph characterizing the topological structure of the design scheme of the frame, through matrix transformations of the displacement vectors, at the transition from local coordinate systems to a global system, it is possible to establish the relationship between the nodal displacements and the displacement increments of individual sections in the direction of the axis of the segment and perpendicular to it. The composition of only three initial matrices of the frame structure, the incidence matrix of the graph, the node coordinate matrix and the matrix of the frame model internal rigidity, solves the problem of automatic formation of the bending moments influence matrix with the help of a PC. The procedure proposed for the construction of the influence matrix, makes it possible to find the forces in the frame structure caused by external load, in the matrix form.

Dynamic characteristics of frame buildings, taking into account the European standards of the Republic of Kazakhstan in construction

The dynamic characteristics of the frame building are considered. As a result of numerical and analytical solutions, the values of the natural frequencies of the transverse vibrations of a singlestorey building, nodal displacements and forces under horizontal seismic actions, taking into account the stiffness diaphragms for various connections with the base, were obtained.

Numerical Assessment of Dented Pipe Using Inline Inspection Data

The current finite element (FE) assessment methods of dented pipes are based on specific dent profiles, which are generally created based on the shape of indenters. However, the actual dent profile in real case scenarios is mostly irregular in shape, depending on the cause of damage. In this paper, FE analyses of dented pipes using inline inspection (ILI) data are presented. Based on the ILI data, the dent profile is generated by applying the nodal displacements to all the pipe nodes. The validation of this nodal displacement approach is discussed in this paper. Besides, a parametric study is carried out to study the behavior of dent for different dent depth, pipe geometry, and pipe grades. The significance of residual stresses generated during the dent formation on the behavior of dented pipe during the service life is also discussed. Finally, the remaining life estimation of dented pipes according to the API 579-1 is presented using FE analysis results.