Abstract
The main goal of building composite materials and structures is to provide appropriate a priori controlled physico-chemical properties. For this purpose, a strengthening is introduced that can bear loads higher than those borne by isotropic materials, improve creep resistance, etc. Composite materials can be designed in a different fashion to meet specific properties requirements.Nevertheless, it is necessary to be careful about the orientation, placement and sizes of different types of reinforcement. These issues should be solved by optimization, which, however, requires the construction of appropriate models. In the present paper we intend to discuss formulations of kinematic and constitutive relations and the possible application of homogenization methods. Then, 2D relations for multilayered composite plates and cylindrical shells are derived with the use of the Euler–Lagrange equations, through the application of the symbolic package Mathematica. The introduced form of the First-Ply-Failure criteria demonstrates the non-uniqueness in solutions and complications in searching for the global macroscopic optimal solutions. The information presented to readers is enriched by adding selected review papers, surveys and monographs in the area of composite structures.
Highlights
Introduction to Macroscopic OptimalDesign in the Mechanics of Composite Materials and Structures Aleksander Muc AbstractThe main goal of building composite materials and structures is to provide appropriate a priori controlled physico-chemical properties
The idea of composite materials arose from the need to combine different materials in order to overcome the shortcomings of each one of them
The progress that has been made in the development of Composite Materials (CM) and its impact on civilization transformations is fast and unusual [1]
Summary
Polymer composites reinforced with unidirectional fibers (1D composites) or textile composites (2D or 3D fiber structures) are heterogeneous (inhomogeneous) materials, since they are made of two or more constituents with different physicochemical properties. A laminate (a lamina) is treated as a material continuum, i.e., there are no discontinuities between material phases or individual layers, air bubbles in a polymeric matrix, micro-cracks, etc We will find this formalism (commonly called macro-mechanics) useful later in the analysis, when dealing with optimization problems. Sci. 2021, 5, 36constants and strain-stress relations are introduced in the material (local) orthogonal coordinate system where the reference axes (x1, x2) are parallel and transverse to the fiber direction (Figure 9)—the so-called on-axis case. I(snshttreQheae1nr1gtdr tahen1f)os ivrsm eEvr1aes treiyo2d1nliors,ewQco,tf1ia2oann dl,ap1omeu rit n1p-2oae1E2,fn -2sdp2iil1ncacu,neleahrloytaogdrtoihntehgmeirsamcteaarrlirapielrdpo(bl1oal2une)met b(sxy1w,aixlv2le)b,ryae weak polymeric matrix To include those effects in the analysis, the stress-strain relations in the k-th layer have to be described with the use of a larger number of engineering constants than previously.
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