TY  - EJOU
AU  - Chen, Haibo 
AU  - Jiang, Fuhang 

TI  - A	Shape	Optimization Approach for	3D Doubly-Periodic	Multi-Layered	 Systems
T2  - The International Conference on Computational \& Experimental Engineering and Sciences

PY  - 2023
VL  - 26
IS  - 1
SN  - 1933-2815

AB  - Acoustic	wave	propagation	has	been	the	subject	of	many	studies	in	engineering	and	physics.	Researchers	
have	 shown	an	increased	interest in	 recent	 years	in	 the	acoustic	 scattering	 of	 periodic	 systems,	 such	as	
phononic	crystals	and	metamaterials [1].	These	artificial	periodic	systems	possess	some	particular	acoustic	
characteristics	 including	 noise	 control,	 waveguides	 and	 negative	 refraction,	 which	 manifest	 excellent	
potential	 applicability	 in	 acoustic	 engineering. Based	 on the isogeometric acoustic	 boundary	 element	
method (BEM) [2],	 an efficient shape	 optimization approach is	 proposed in	 this	 research for	 threedimensional	doubly-periodic	multi-layered	systems.	The	interfaces between	different	acoustic	mediums	are
infinite	doubly	periodic	surfaces,	which	can	be	constructed	by	open	non-uniform	rational	B-splines	(NURBS)	
surfaces.	We	develop	a periodic	isogeometric BEM	for	the	sound	field	analysis	of	the	doubly-periodic	multilayered	 system.	 The	 sound	 transmission	 and	 quasi-periodic	 boundary	 conditions	 are	 considered in	 the	
proposed	method and	the	Ewald	method	is	employed	to	accelerate	the	calculation	of	periodic	green	function.	
By	imposing	 shape	 perturbation	 and	 using	 the	 adjoint	 variable	method,	the	 shape	 derivative	 formula is	
derived	for the	doubly-periodic	multiple	boundaries.	The	control	points	of	the	NURBS	surfaces	are	selected
as	 the	 shape	 design	 variables,	 and	 all	 shape	 sensitivities	 can	 be	 calculated	 by	 discretizing	 the	 shape	
derivative	 formula.	 Finally,	 the	 corresponding	 shape	 optimization	 problem	 is	 solved	 by	 the	 method	 of	
moving	asymptotes.	Numerical	tests	validate	the	accuracy	and	applicability	of	the	proposed	approach.
KW  - Doubly-periodic	multi-layered	system;	shape	optimization;	isogeometric	boundary	element	method;	shape derivative;	adjoint	variable	method

DO  - 10.32604/icces.2023.09414