Influence of the molding angle on tensile properties of FDM parts with orthogonal layering

Fused deposition molding (FDM) is one of the most widely used three‐dimensional (3D) printing technologies. This paper explores the influence of the forming angle on the tensile properties of FDM specimens. Orthogonal layering details were studied through experiments, theory, and finite element simulations. The stiffness and strength of the specimens were analyzed using the classical laminated plate theory and the Tsai–Wu failure criterion. The experimental process was simulated using finite element simulations. Results show that it is feasible to predict the stiffness and strength of FDM specimens using classical laminated plate theory and the Tsai–Wu failure criterion. A molding angle of 45° leads to specimens with maximized tensile properties. Numerical simulations show that changing the molding angle changes the internal stress and deformation fields inside samples, leading to FDM samples with different mechanical properties due to the orthogonal layers at different molding angles.     

PBL节点初始平动刚度计算及设计参数优化

为研究钢桁腹混凝土组合箱梁中PBL(Perfobond Leiste)节点的初始平动刚度及其影响因素,首先基于组件法,运用卡氏第二定理推导出考虑了开孔钢板与混凝土间的界面剪切力和混凝土榫贡献的PBL节点的初始平动刚度表达式,其次以某工程实例为背景,结合有限元模型验证所推公式的合理性;在此基础上分析了混凝土强度、腹杆直径、腹杆壁厚、开孔钢板开孔孔径和开孔钢板厚度等构造参数对初始平动刚度的影响,并利用正交分析法对以上5个参数进行优化组合。研究结果表明,本文方法计算的PBL节点初始平动刚度结果与有限元计算结果间的误差在8.0%以内;相较运用解三角形计算腹杆平动位移的方法,采用卡氏第二定理不仅可以简化计算,还可以减小解三角形过程中因多次计算变形带来的误差累积;腹杆刚度对PBL节点整体平动刚度的贡献最大,可达到82.5%;保持原设中的混凝土强度不变,将腹杆直径增加20 mm,将钢腹杆壁厚增加4 mm,将开孔钢板开孔孔径增加4 mm,将开孔钢板厚度增加4 mm,可以将PBL节点理论初始平动刚度提高约25.7%。     

Wavelets with differential relation

Divergence-free wavelets are successfully applied to numerical solutions of Navier-Stokes equation and to analysis of incompressible flows. They closely depend on a pair of one-dimensional wavelets with some differential relations. In this paper, we point out some restrictions of those wavelets and study scaling functions with the differential relation; Wavelets and their duals are discussed; In addition to the differential relation, we are particularly interested in a class of examples with the interpolatory property; It turns out there is a connection between our examples and Micchelli’s work.     

Newton's method on Riemannian manifolds and a geometric model for the human spine

To study a geometric model of the human spine we are led tofinding a constrained minimum of a real valued function definedon a product of special orthogonal groups. To take advantgeof its Lie group structure we consider Newton's method on thismanifold. Comparisons between measured spines and computed spinesshow the pertinence of this approach.     

Cyclic Designs with Block Size 4 and Related Optimal Optical Orthogonal Codes

We prove the existence of a cyclic (4p, 4, 1)-BIBD—and hence, equivalently, that of a cyclic (4, 1)-GDD of type 4 ^p —for any prime such that (p–1)/6 has a prime factor q not greater than 19. This was known only for q=2, i.e., for . In this case an explicit construction was given for . Here, such an explicit construction is also realized for .We also give a strong indication about the existence of a cyclic (4p 4, 1)-BIBD for any prime , p>7. The existence is guaranteed for p>(2q ³–3q ²+1)²+3q ² where q is the least prime factor of (p–1)/6.Finally, we prove, giving explicit constructions, the existence of a cyclic (4, 1)-GDD of type 6 ^p for any prime p>5 and the existence of a cyclic (4, 1)-GDD of type 8 ^p for any prime . The result on GDD's with group size 6 was already known but our proof is new and very easy.All the above results may be translated in terms of optimal optical orthogonal codes of weight four with =1.     

Quincunx fundamental refinable functions and quincunx biorthogonal wavelets

We analyze the approximation and smoothness properties of quincunx fundamental refinable functions. In particular, we provide a general way for the construction of quincunx interpolatory refinement masks associated with the quincunx lattice in . Their corresponding quincunx fundamental refinable functions attain the optimal approximation order and smoothness order. In addition, these examples are minimally supported with symmetry. For two special families of such quincunx interpolatory masks, we prove that their symbols are nonnegative. Finally, a general way of constructing quincunx biorthogonal wavelets is presented. Several examples of quincunx interpolatory masks and quincunx biorthogonal wavelets are explicitly computed.

     

On the Right-Definite and Left-Definite Spectral Theory of the Legendre Polynomials

In this paper, we further develop the left-definite and right-definite spectral theory associated with the self-adjoint differential operator A in L²(-1,1), generated from the classical second-order Legendre differential equation, having the sequence of Legendre polynomials as eigenfunctions. Specifically, we determine the first three left-definite spaces associated with the pair (L²(-1,1),A). As a consequence of these results, we determine the explicit domain of both the associated left-definite operator A₁, first observed by Everitt, and the self-adjoint operator A^1/2. In addition, we give a new characterization of the domain D(A) of A and, as a corollary, we present a new proof of the Everitt-Mari result which gives optimal global smoothness of functions in D(A).     

Group Representation of Waves in Gyrotropic Crystals

A new group (linear) representation of the propagation of waves in properly and naturally gyrotropic crystals in the general case where the nonreciprocity effect takes place has been developed. Simple expressions of the dependence of ray (group) velocities and polarization vectors of isonormal waves on the complex vector of principal velocities dual to the unitary tensor by which the optical properties of crystals are directly characterized have been obtained. The relationship between gyrotropy and anisotropy and the dipole moment and displacement current induced by the radiation in the crystal has been established. It is shown that the presence of gyrotropy and nonlinear polarization of radiation together with the elimination of conical points entails a phase ambiguity of the ray velocity of the quantummechanical type and a smearing and layering of the wave surface, as well as a discreteness of the spectrum of velocity values of isonormal waves.     

Multi-Fractal Formalism for Quasi-Self-Similar Functions

The study of multi-fractal functions has proved important in several domains of physics. Some physical phenomena such as fully developed turbulence or diffusion limited aggregates seem to exhibit some sort of self-similarity. The validity of the multi-fractal formalism has been proved to be valid for self-similar functions. But, multi-fractals encountered in physics or image processing are not exactly self-similar. For this reason, we extend the validity of the multi-fractal formalism for a class of some non-self-similar functions. Our functions are written as the superposition of similar structures at different scales, reminiscent of some possible modelization of turbulence or cascade models. Their expressions look also like wavelet decompositions. For the computation of their spectrum of singularities, it is unknown how to construct Gibbs measures. However, it suffices to use measures constructed according the Frostman's method. Besides, we compute the box dimension of the graphs.