LEADER 04156nam 22005655 450 001 9911034942303321 005 20251013130433.0 010 $a3-031-98052-2 024 7 $a10.1007/978-3-031-98052-7 035 $a(MiAaPQ)EBC32345908 035 $a(Au-PeEL)EBL32345908 035 $a(CKB)41640983900041 035 $a(DE-He213)978-3-031-98052-7 035 $a(EXLCZ)9941640983900041 100 $a20251013d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Simplified Approach to the Classical Laminate Theory of Composite Materials $eApplication of Bar and Beam Elements /$fby Andreas Öchsner 205 $a2nd ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (260 pages) 225 1 $aAdvanced Structured Materials,$x1869-8441 ;$v242 311 08$a3-031-98051-4 327 $aIntroduction -- Bar Elements -- Euler-Bernoulli Beam Elements -- Combination of Bar and Beam Elements -- Classical Laminate Theory for One-Dimensional Elements -- Example Problems -- Outlook to the Two-Dimensional Case. 330 $aThis book provides a systematic introduction to composite materials, which are obtained by a layer-wise stacking of one-dimensional bar/beam elements. Each layer may have different mechanical properties, but each single layer is considered as isotropic. The major idea is to provide a simplified theory to easily understand the classical two-dimensional laminate theory for composites based on laminae with unidirectional fibers. In addition to the elastic behavior, failure is investigated based on the maximum stress, maximum strain, Tsai-Hill, and the Tsai-Wu criteria. Partial differential equations lay the foundation to mathematically describe the mechanical behavior of any classical structural member known in engineering mechanics, including composite materials. The so-called classical laminate theory provides a simplified stress analysis, and a subsequent failure analysis, without the solution of the system of coupled differential equations for the unknown displacements. The procedure provides the solution of a statically indeterminate system based on a generalized stress?strain relationship under consideration of the constitutive relationship and the definition of the so-called stress resultants. This laminate theory is typically provided for two-dimensional plane problems, where the basic structural element is a simple superposition of a classical plane elasticity element with a thin plate element under the consideration of an orthotropic constitutive law. This two-dimensional approach and the underlying advanced continuum mechanical modeling might be very challenging for some students, particularly at universities of applied sciences. Thus, a reduced approach, the so-called simplified classical laminate theory, has been developed. The idea is to use solely isotropic one-dimensional elements, i.e., a superposition of bar and beam elements, to introduce the major calculation steps of the classical laminate theory. Understanding this simplified theory is much easier and the final step it to highlight the differences when moving to the general two-dimensional case. 410 0$aAdvanced Structured Materials,$x1869-8441 ;$v242 606 $aContinuum mechanics 606 $aComposite materials 606 $aMathematics$xData processing 606 $aContinuum Mechanics 606 $aComposites 606 $aComputational Science and Engineering 615 0$aContinuum mechanics. 615 0$aComposite materials. 615 0$aMathematics$xData processing. 615 14$aContinuum Mechanics. 615 24$aComposites. 615 24$aComputational Science and Engineering. 676 $a620.118 700 $aÖchsner$b Andreas$0317948 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911034942303321 996 $aA Simplified Approach to the Classical Laminate Theory of Composite Materials$93568531 997 $aUNINA