Narrow Results

Stiffened shallow spherical shell has the advantages including high strength and light weight, which allows it to be widely applied in areas including aerospace, submarine and civil engineering. For the design of scaled model for elastic–plastic buckling of a large radially–circumferentially stiffened shallow spherical shell under uniformly distributed pressure and for the purpose of similarity prediction, the similarity relation of the elastic–plastic buckling coefficient of the shell is derived; then by using the dense stiffening theory and considering the dual nonlinearity of geometry and materials, the energy increment formula for the structure under uniformly distributed external pressure is established; next, based on the similarity transformation of the energy increment of the structural system, the generalized similarity condition and similarity relation of elastic–plastic buckling of the structure under uniformly distributed external pressure are identified. Based on the scaling and equivalence of tensile–compressive stiffness and bending stiffness, the distortion scaled model for the prototype is designed. Through numerical simulation, the distortion similarity prediction for elastic–plastic buckling under uniformly distributed pressure of the radially–circumferentially stiffened shallow spherical shell that has square-shaped dimple defects has been conducted; based on the derived similarity relation of elastic–plastic buckling of stiffened plate, the similarity prediction for the elastic–plastic buckling of orthogonally stiffened plate in the plane under unidirectional uniformly distributed pressure has been conducted. The results indicate that the load–displacement curve, buckling load, and buckling mode of the distortion similarity scaled model, combined with the established radial displacement scaling factor expression, the scaling relation of tension–compression stiffness, and the similarity relation of buckling mode, can effectively predict the elastic–plastic buckling characteristics of its prototype structure. The research results can provide theoretical reference for the design and test of the scaled model with distortion of elastic–plastic buckling of similar stiffened large shell structures.

A novel analytical method for evaluating the buckling stability of the pier–cap–pile system under scour effect is proposed, and furthermore, the concept of rapid assessment of bridge buckling stability based on natural frequency is innovatively introduced in this paper. First, the total potential energy function of the bridge pier–cap–pile system is established, and the closed-form solution of structural system critical buckling load under scouring is solved according to the principle of stationary potential energy. Second, the sensitivity analyses of pier height, pier width, bending stiffness reduction in pier, pile slenderness ratio, pile bending stiffness reduction, m-value of soil and structural gravity to the buckling load are carried out. On this basis, 60 sets of sensitive parameter sample combinations are extracted by the Latin Hypercube Sampling algorithm, and a proxy model relating the critical buckling load to scour depth and the sensitive parameters are then developed using the McQuarter global optimization algorithm. Finally, the regression relationship model between the critical buckling load and the natural frequency is formed by combining the proxy model and the existing relationship between the scour depth and the first-order natural frequency. The feasibility of the proposed assessment method is demonstrated by the finite element method using a bridge case study, which provides an insight and a new means of quantitatively evaluating the safety of bridges under scour effect.

This paper presents an experimental, numerical, and theoretical investigation of cold-formed steel face-to-face built-up columns (CFS-FBC). Twelve global buckling built-up columns with different lengths and screw arrangements were experimentally studied. According to the test results, the load-bearing capacity of CFS-FBC was significantly affected by the arrangement of screws. Decreasing screw spacing from 300mm to 200mm resulted in a 1–5% increase in load-bearing capacity, while further reducing it to 100mm led to an increase of 10–20%. Numerical models were created and calibrated based on compression tests, with parametric analyses conducted to further explore the influence of screw arrangements. It was demonstrated that the most effective method to improve the global buckling behavior of the CFS-FBC was reducing the screw spacing. The theoretical elastic global buckling load of CFS-FBC was derived based on the energy method, taking into account screw arrangements and shearing stiffness. The derived buckling load was compared with the simulation results to validate its accuracy, and then it was introduced into the AISI-S100 design framework to calculate the load-bearing capacity of CFS-FBC. It was found that the proposed method has excellent advantages in accuracy and effectiveness. A reliability analysis was carried out to indicate that the proposed method was on the safety side in predicting the load-bearing capacity of CFS-FBC.

We present an efficient method for computing acoustic energy within complex-shaped geometries and cavities with obstacles in the mid-high frequency range. This method is based on the Simplified Energy Method (MES), known for its accuracy in such frequency ranges but traditionally limited to simple cavity shapes. The proposed hybrid method integrates the techniques of ray and triangle intersection with the MES formulation to address these limitations. By calculating the intersection points of the rays, we identify the obstructing elements before computing the energy transfer between the boundary elements. A primary intersection state matrix, containing direct view information between elements, is integrated into a modified MES equation to eliminate unnecessary computations and ensure precise calculations of energy transfer for obstructed elements. This hybrid approach is applied to both direct and reverberant fields to determine the total energy density. Numerical simulations conducted within a complex domain enclosure demonstrate the precision of the proposed algorithms when compared to traditional MES calculations. In addition, we propose applying this method to robust shape optimization, effectively balancing competing criteria to achieve optimized acoustic performance. This refined and computationally feasible tool significantly advances computational acoustics, providing accurate and efficient design solutions for complex environments.

Small-amplitude weakly coupled oscillators of the Klein–Gordon lattices are approximated by equations of the discrete nonlinear Schrödinger type. We show how to justify this approximation by two methods, which have been very popular in the recent literature. The first method relies on a priori energy estimates and multi-scale decompositions. The second method is based on a resonant normal form theorem. We show that although the two methods are different in the implementation, they produce equivalent results as the end product. We also discuss the applications of the discrete nonlinear Schrödinger equation in the context of existence and stability of breathers of the Klein–Gordon lattice.

The problem of penetrative convection in fluid layer with vertical throughflow effect is studied by using methods of linear instability theory and unconditional and conditional nonlinear energy theories. Then, the accuracy of the linear instability thresholds are tested using a three-dimensional simulation. For small values of throughflow, the results support the assertion that the linear theory is a good prediction to the onset of convective motion, and thus, regions of stability. However, for large values of throughflow, we found that the actual threshold move from the linear instability threshold with increasing the positive and negative effect of throughflow.

For the 𝔰𝔬(4) free rigid body the stability problem for the isolated equilibria has been completely solved using Lie-theoretical and topological arguments. For each case of nonlinear stability previously found, we construct a Lyapunov function. These Lyapunov functions are linear combinations of Mishchenko's constants of motion.

In this paper, we consider a one-dimensional half-space problem for a system of viscous conservation laws which is deduced to a symmetric hyperbolic–parabolic system under assuming that the system has a strictly convex entropy function. We firstly prove existence of a stationary solution by assuming that a boundary strength is sufficiently small. The existence of the stationary solution is characterized by the number of negative characteristics. In the case where one characteristic speed is zero at spatial asymptotic state $x\to \infty$, we assume that the characteristic field corresponding to the characteristic speed 0 is genuinely nonlinear in order to show existence of a degenerate stationary solution with the aid of a center manifold theory. We next prove that the stationary solution is time asymptotically stable under a smallness assumption on an initial perturbation in the Sobolev space. The key to proof is to derive the uniform a priori estimates by using the energy method, where the stability condition of Shizuta–Kawashima type plays an essential role.

This paper deals with the analysis of the behavior of a Spherical Harmonics Expansion (SHE) model associated with an oscillating electrostatic potential.

We consider the stability of control prescribed by hybrid PDE–ODE systems modeling intermittent hormonal therapy of prostate cancer. Hybrid systems can be regarded as a generalization of optimal control. However, since the purpose of hybrid systems is not only minimization or maximization of a corresponding functional, it is not clear what is optimal in hybrid systems. In this paper, we shall give a concept of stability of the control prescribed by the hybrid PDE–ODE systems. Moreover, we show a sufficient condition on initial data for the existence of the stable control. Finally, we apply the main result to several mathematical models describing intermittent hormonal therapy of prostate cancer.

We present and analyze new multi-species phase-field mathematical models of tumor growth and ECM invasion. The local and nonlocal mathematical models describe the evolution of volume fractions of tumor cells, viable cells (proliferative and hypoxic cells), necrotic cells, and the evolution of matrix-degenerative enzyme (MDE) and extracellular matrix (ECM), together with chemotaxis, haptotaxis, apoptosis, nutrient distribution, and cell-to-matrix adhesion. We provide a rigorous proof of the existence of solutions of the coupled system with gradient-based and adhesion-based haptotaxis effects. In addition, we discuss finite element discretizations of the model, and we present the results of numerical experiments designed to show the relative importance and roles of various effects, including cell mobility, proliferation, necrosis, hypoxia, and nutrient concentration on the generation of MDEs and the degradation of the ECM.

This paper deals with the behavior of acoustic cavities in the mid-high frequency range. The method proposed here is based on an energy flow method named Simplified Energy Method (MES). MES method is quite efficient in the mid-high frequency range but the directivity of the boundary sources is not well estimated. We propose a hybrid method which couples MES and the Boundary Element Method (BEM). Thus, the BEM method is used to estimate the direct field, considering a "correct" directivity. As a complete calculation is not adapted to BEM in mid-high frequency range because of the calculation costs, we only apply BEM on the domains including boundary sources. Other parts of the system and the reverberated field are estimated by the mean of MES method. This hybrid method leads to a consistent prediction of injected power densities. Numerical comparisons prove the efficiency of the proposed reformulation.

This paper deals with shape optimization issues under vibroacoustic criteria. The aim of the conducted research is to minimize the energy density in the cavity by changing its geometry parameters. The energy density is obtained through an energy method called simplified energy method (MES). The optimization method is based on a transformation function mapping 3D cavity surface on a 2D domain. The optimization process directly relies on this function and thus avoids remeshing of the geometry. The proposed method allows to describe the geometry through Bezier, Bspline and NURBS parametrization. To illustrate the method, we process a shape optimization on a simple acoustic cavity.

This paper is concerned with the problem of obtaining a unique solution for radiation at irregular frequencies when an integral equation of frequency averaged quadratic pressure (FAQP) is used to get robust predictions at medium and high frequencies. It is proved that there is no unique solution of the integral equation of FAQP at irregular frequencies, and existence and uniqueness of solutions under four types of boundary conditions are discussed. A combined energy boundary integral equation formulation (CEBIEF) is presented and proves to be efficient to overcome the nonuniqueness of the integral equation of FAQP. The numerical examples are given to demonstrate the versatility of the CEBIEF method with a proposed function correctly indicating a solution.

We give a description of singularity formation in terms of energy quanta for 2-dimensional radially symmetric equivariant harmonic map heat flows. Adapting Struwe's energy method we first establish a finite bubble tree result with a discrete multiple of energy quanta disappearing in the singularity. We then use intersection-comparison arguments to show that the bubble tree consists of a single bubble only and that there is a well defined scale R_BHK(t) ↓ 0 in which the solution converges to the standard harmonic map.

We consider the Cauchy problem of a third order in time nonlinear equation known as the Jordan–Moore–Gibson–Thompson (JMGT) equation arising in acoustics as an alternative model to the well-known Kuznetsov equation. We show a local existence result in appropriate function spaces, and, using the energy method together with a bootstrap argument, we prove a global existence result for small data, without using the linear decay. Finally, polynomial decay rates in time for a norm related to the solution will be obtained.

Based on the energy principle, a theoretical study of the elastic lateral distortional buckling (LDB) and restrained distortional buckling (RDB) of I-beams is presented. First, because the existing potential energy expressions for LDB are not suitable for members under a transverse distributed load, a new general potential energy expression of I-beams for lateral buckling is derived by using the nonlinear elastic theory. The proposed expression is equivalent to the classical potential equation when web distortion is suppressed and caters for I-beams under transverse distributed load, transverse concentrated load, and end moments, and when the web is flexible. Then, an LDB equation for simply supported, doubly symmetric, I-beams under uniform distributed load is developed by invoking the Ritz method. In addition, an RDB equation for continuous composite beams is also deduced by using some simplifications. The corresponding simplifications and equations are verified by the finite element method. Suggestions for further study are also presented. The outcomes of the present paper have important theoretical and practical significance and provide a rational basis for practical design methods.

In this paper, explicit local buckling analysis of orthotropic plates subjected to uniaxial compression with two loaded edges simply-supported and two unloaded edges supported by combined vertical and rotational restraining springs is presented. Based on the total potential energy function, the eigenvalue problem is formulated by treating the buckled shape functions as the admissible functions that satisfy the boundary conditions of the rectangular plates. Closed-form and approximate local buckling solutions of the combined rotationally- and vertically-restrained orthotropic plates, as well as explicit formulas for the critical buckling load and critical aspect ratio under the uniform compression, are obtained. By adjusting the stiffness of the rotational and vertical restraining springs, explicit local buckling solutions are established for eight simple cases of boundary conditions. To verify the explicit solutions, numerical analyses of orthotropic plates using the exact transcendental and finite element methods are conducted, for which reasonable agreement has been obtained between the explicit and numerical solutions, particularly for the simplified cases. The explicit solution obtained in this study can be used to facilitate the buckling analysis of composite laminated structures with different boundary conditions or joint connections as parts of stiffened and thin-walled structures by treating them as discrete plates with restrained boundary conditions.

This paper presents a novel approach for determining the critical lateral-torsional buckling loads of beams subjected to arbitrarily transverse loads. This new method is developed based on the classical energy method. However, the difference of the present method from the traditional energy methods is the formulation of potential energy of external loads, which is expressed in terms of the internal bending moment and internal shear force in the pre-buckling stage regardless of the type of loading. Compared to the traditional formulations of the potential energy of external loads, not only is the present formula simple in the form, easy and convenient in the calculation, but it also provides a unified form for calculating accurate critical load of lateral-torsional buckling of the beams.

This paper presents an improved generalized procedure for dealing with the stability of thin-walled beams under combined symmetric loads based on the energy method. The differential equations for the case of complex loading conditions were developed using an axis transformation matrix. The work caused by external loads was related to the work of internal forces to simplify the computational procedure. The thin-walled beam subjected to axial force $F$, bending moment $M$ at both ends, and concentrated load $P$ at midspan was studied. The case of a concentrated load $P$ replaced by a distributed load $q$ over partial beam length was also examined. The stability region boundary of the beam was derived by two approaches: one was to estimate an approximate angle of twist prior to determination of the deflection and the other was to do it in the reverse way. Numerical results reveal that the first approach yields less error than the second; however, the outcome obtained by the former was more cumbersome than the latter. Above all, both approaches provided feasible results and are useful for further applications dealing with the stability analysis of thin-walled beams.