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From the natural continuum to the elastic spring cell in three and two dimensions - a flexibility approach

机译:从自然连续体到三个和两个维度的弹性弹簧单元 - 一种灵活性的方法

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Purpose The employment of spring cell substitutes for the numerical analysis of solids and structures in place of finite elements has occasioned research on the subject with regard to both, the applicability of existing approaches and the advancement of concepts. This paper aims to explore in the context of linear elasticity the substitution of the simplex tetrahedral element in space and the triangle in the plane by corresponding spring cells deduced on a flexibility basis using the natural formalism. Design/methodology/approach The natural formalism is characterized by the homogeneous definition of strain and stress along the lines connecting nodes of the simplex tetrahedron and the triangle. The elastic compliance involves quantities along the prospective spring directions and offers itself for the transition to the spring cell. The diagonal entities are interpreted immediately as spring flexibilities, the off-diagonal terms account for the completeness of the substitution. In addition to the isotropic elastic material, the concept is discussed for anisotropic elasticity in the plane. Findings The natural point of view establishes the spring cell as part of the continuum element. The simplest configuration of pin-joined bars discards all geometrical and physical cross effects. The approach is attracting by its transparent simplicity, revealing deficiencies of the spring cell and identifying directly conditions for the complete substitution of the finite element.Research limitations/implications - The spring cell counterparts of the tetrahedral- and the triangular finite elements allow employment in problems in three and two dimensions. However, the deficient nature of the approximation requires attention in the design of the discretization lattice such that the conditions of complete finite element substitution are approached as close as possible. Practical implications - Apart from plane geometries, triangular spring cells have been assembled to lattice models of space structures such as membrane shells and similar. Tetrahedral cells have been used, in modelling plates and shell structures exhibiting bending stiffness.Originality/value The natural formalism of simplex finite elements in three and two dimensions is used for defining spring cells on a flexibility basis and exploring their properties. This is a novel approach to spring cells and an original employment of the natural concept in isotropic and anisotropic elasticity.
机译:目的,用于在有限元的固体和结构代替固体和结构的数值分析的春细替代物的就业已经过时了解了关于现有方法的适用性和概念的进步的主题。本文旨在探讨线性弹性的背景下,使用自然形式主义在灵活性基础上推导出平面中的空间和三角形的单纯形四面体元件的替代。设计/方法/方法自然形式主义的特征在于,沿着单纯x四面体的节点和三角形的线条的均匀定义和应力的均匀定义。弹性顺应性涉及沿着前瞻性弹簧方向的数量,并为其自身提供到弹簧电池的过渡。对角线实体被解释为Spring Flexibilities,非对角线术语算用于替换的完整性。除了各向同性弹性材料之外,讨论该概念在平面中用于各向异性弹性。发现自然的观点是作为连续元件的一部分的弹簧单元。销连接条的最简单配置丢弃了所有几何和物理交叉效果。该方法是通过其透明简单吸引,揭示了弹簧电池的缺陷,并识别有限元完全取代的直接条件。研究限制/影响 - 四面体和三角形有限元的弹簧电池对应物允许就业问题在三个和两个维度。然而,近似的不足性质需要注意的是离散化格的设计,使得完全有限元替换的条件尽可能接近。实际意义 - 除了平面几何形状之外,三角形弹簧电池已经组装成空间结构的晶格模型,如膜壳和相似。已经使用了四面体电池,在造型板和壳体结构中,呈现弯曲刚度。物流/值三个和两个尺寸中的单纯性有限元的自然形式主义用于限定弹簧电池,以灵活地确定并探索其性质。这是一种新的春季细胞方法以及各向同性和各向异性弹性的自然概念的原始就业。

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